Quantum Critical Research Articles

Bridging quantum criticality via many-body scarring

Quantum dynamics in certain kinetically-constrained systems can display a strong sensitivity to the initial condition, wherein some initial states give rise to persistent quantum revivals -- a type of weak ergodicity breaking known as `quantum many-body scarring' (QMBS). Recent work [Phys.Rev.B 105, 125123 (2022)] pointed out that QMBS gets destroyed by tuning the system to a quantum critical point, echoing the disappearance of long-range order in the system's ground state at equilibrium. Here we show that this picture can be much richer in systems that display QMBS dynamics from a continuous family of initial conditions: as the system is tuned across the critical point while at the same time deforming the initial state, the dynamical signatures of QMBS at intermediate times can undergo an apparently smooth evolution across the equilibrium phase transition point. We demonstrate this using the PXP model -- a paradigmatic model of QMBS that has recently been realized in Rydberg atom arrays as well as ultracold bosonic atoms in a tilted optical lattice. Using exact diagonalization and matrix product state methods, we map out the dynamical phase diagram of the PXP model with the quenched chemical potential. We demonstrate the existence of a continuous family of initial states that give rise to QMBS and formulate a ramping protocol that can be used to prepare such states in experiment. Our results show the ubiquity of scarring in the PXP model and highlight its intriguing interplay with quantum criticality.

Quantum criticality induced strong coupling between resonant modes

We propose a scheme to achieve a strong interaction between an optical cavity and a single polariton mode of an optomechanical cavity, despite a weak initial coupling between the two. This interaction is made possible by quantum criticality, and the coupled system comprising two optical cavities and an optomechanical cavity displays a phenomenon similar to the concepts of electromagnetically induced transparency (EIT) and Autler–Townes splitting in atomic physics.

Dynamical quantum phase transitions in Stark quantum spin chains

We investigate the nonequilibrium dynamics of one-dimension spin models in the presence of a uniform force. The linear potential induces delocalization-localization transition in the free particles model which is known as the Wannier-Stark effect. We study dynamical quantum phase transition (DQPT) due to sudden global quenches across a quantum critical point when the system undergoes a localization-delocalization transition. In this regard, we consider the XX and XXZ spin chains and explore two types of quenches with and without ramping through the delocalization-localization point. The XX model was mapped to the free fermion particles, so both analytical and numerical results were provided. Results unveil that the dynamical signature of localization-delocalization transition can be characterized by the nonanalyticities in dynamical free energy (corresponds to the zero points in the Loschmit echo). We also explore the interaction effects considering XXZ spin chains, using the time-dependent extension of the numerical DMRG technique. Our results show that depending on the anisotropic parameter $\Delta\lessgtr1.0$, if both the initial and post-quench Hamiltonian are in the same phase or not, DQPTs may happen. Moreover, the interrelation between DQPTs with different correlation measures such as the equilibrium order parameters or entanglement entropy production of the system remains unclear. We provide more analyses on the feature of DQPTs, in both types of quenches, by connecting them to the average local magnetization, entanglement entropy production, and the Schmidt gap.

The breakdown of both strange metal and superconducting states at a pressure-induced quantum critical point in iron-pnictide superconductors

Here we report the first observation of the concurrent breakdown of the strange metal (SM) normal state and superconductivity at a pressure-induced quantum critical point in Ca10(Pt4As8)((Fe0.97Pt0.03)2As2)5 superconductor. We find that, upon suppressing the superconducting state, the power exponent (α) changes from 1 to 2, and the slope of the temperature-linear resistivity per FeAs layer (A□) gradually diminishes. At a critical pressure, A□ and superconducting transition temperature (Tc) go to zero concurrently, where a quantum phase transition from a superconducting state with a SM normal state to a non-superconducting Fermi liquid state occurs. Scaling analysis reveals that the change of A□ with Tc obeys the relation of Tc ~ (A□)0.5, similar to what is seen in other chemically doped unconventional superconductors. These results suggest that there is a simple but powerful organizational principle of connecting the SM normal state with the high-Tc superconductivity.

Reconciling scaling of the optical conductivity of cuprate superconductors with Planckian resistivity and specific heat

Materials tuned to a quantum critical point display universal scaling properties as a function of temperature T and frequency ω. A long-standing puzzle regarding cuprate superconductors has been the observed power-law dependence of optical conductivity with an exponent smaller than one, in contrast to T-linear dependence of the resistivity and ω-linear dependence of the optical scattering rate. Here, we present and analyze resistivity and optical conductivity of La2−xSrxCuO4 with x = 0.24. We demonstrate ℏω/kBT scaling of the optical data over a wide range of frequency and temperature, T-linear resistivity, and optical effective mass proportional to sim ln T corroborating previous specific heat experiments. We show that a T, ω-linear scaling Ansatz for the inelastic scattering rate leads to a unified theoretical description of the experimental data, including the power-law of the optical conductivity. This theoretical framework provides new opportunities for describing the unique properties of quantum critical matter.

Dielectric Relaxation by Quantum Critical Magnons.

We report the experimental observation of dielectric relaxation by quantum critical magnons. Complex capacitance measurements reveal a dissipative feature with a temperature-dependent amplitude due to low-energy lattice excitations and an activation behavior of the relaxation time. The activation energy softens close to a field-tuned magnetic quantum critical point at H=H_{c} and follows single-magnon energy for H>H_{c}, showing its magnetic origin. Our study demonstrates the electrical activity of coupled low-energy spin and lattice excitations, an example of quantum multiferroic behavior.

Triangular Kondo lattice in YbV6Sn6 and its quantum critical behavior in a magnetic field

We report on the magnetization, specific heat, and electrical resistivity for a newly discovered heavy-fermion (HF) compound, ${\mathrm{YbV}}_{6}{\mathrm{Sn}}_{6}$, which is crystallized in a hexagonal ${\mathrm{HfFe}}_{6}{\mathrm{Ge}}_{6}$-type structure, highlighted by the stacking of the triangular ytterbium sublattice and kagome vanadium sublattice. Above 2 K, ${\mathrm{YbV}}_{6}{\mathrm{Sn}}_{6}$ shows typical HF properties due to the Kondo effect on the Kramers doublet of ${\mathrm{Yb}}^{3+}$ ions in the crystalline electric field. A remarkable magnetic ordering occurs at ${T}_{\mathrm{N}}=0.40$ K in zero field, while a weak external field suppresses the ordering and induces non-Fermi-liquid behavior. In strong magnetic field, the compound shows a heavy Fermi-liquid state. ${\mathrm{YbV}}_{6}{\mathrm{Sn}}_{6}$ is represented as one of the few examples of Yb-based HF compounds hosting a triangular Kondo lattice on which a magnetic field induces quantum criticality near zero temperature.

Detecting quantum critical points at finite temperature via quantum teleportation

We show that the quantum teleportation protocol is a powerful tool to study quantum phase transitions (QPTs) at finite temperatures. We consider a pair of spins from an infinite spin-1/2 chain (XXZ model) in equilibrium with a reservoir at temperature T as the resource used by Alice and Bob to implement the teleportation protocol. We show that the efficiency of this pair of spins to teleport a qubit is drastically affected after we cross a quantum critical point (QCP), even for high values of T. Also, we show that the present tool is as sharp as quantum discord (QD) to spotlight a QCP, where QD is the best finite T QCP detector known to date. Contrary to QD, however, we show that the present tool is easier to compute theoretically and has a direct experimental and operational meaning.

Topological Fracton Quantum Phase Transitions by Tuning Exact Tensor Network States.

Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable models remains a formidable challenge. Here we employ an exact 3D quantum tensor-network approach that allows us to study a Z_{N} generalization of the prototypical X cube fracton model and its quantum phase transitions between distinct topological states via fully tractable wave function deformations. We map the (deformed) quantum states exactly to a combination of a classical lattice gauge theory and a plaquette clock model, and employ numerical techniques to calculate various entanglement order parameters. For the Z_{N} model we find a family of (weakly) first-order fracton confinement transitions that in the limit of N→∞ converge to a continuous phase transition beyond the Landau-Ginzburg-Wilson paradigm. We also discover a line of 3D conformal quantum critical points (with critical magnetic flux loop fluctuations) which, in the N→∞ limit, appears to coexist with a gapless deconfined fracton state.

Revealing the finite-frequency response of a bosonic quantum impurity

Quantum impurities are ubiquitous in condensed matter physics and constitute the most stripped-down realization of many-body problems. While measuring their finite-frequency response could give access to key characteristics such as excitations spectra or dynamical properties, this goal has remained elusive despite over two decades of studies in nanoelectronic quantum dots. Conflicting experimental constraints of very strong coupling and large measurement bandwidths must be met simultaneously. We get around this problem using cQED tools, and build a precisely characterized quantum simulator of the boundary sine-Gordon model, a non-trivial bosonic impurity problem. We succeeded to fully map out the finite frequency linear response of this system. Its reactive part evidences a strong renormalisation of the nonlinearity at the boundary in agreement with non-perturbative calculations. Its dissipative part reveals a striking many-body broadening caused by multi-photon conversion. The experimental results are matched quantitatively to a perturbative calculation based on a microscopically calibrated model. Furthermore, we push the device into a regime where perturbative calculations break down, which calls for more advanced theoretical tools to model many-body quantum circuits. We also critically examine the technological limitations of cQED platforms to reach universal scaling laws. This work opens exciting perspectives for the future such as quantifying quantum entanglement in the vicinity of a quantum critical point or accessing the dynamical properties of non-trivial many-body problems.

Proximate deconfined quantum critical point in SrCu2(BO3)2.

The deconfined quantum critical point (DQCP) represents a paradigm shift in quantum matter studies, presenting a "beyond Landau" scenario for order-order transitions. Its experimental realization, however, has remained elusive. Using high-pressure 11B nuclear magnetic resonance measurements on the quantum magnet SrCu2(BO3)2, we here demonstrate a magnetic field-induced plaquette singlet to antiferromagnetic transition above 1.8 gigapascals at a notably low temperature, Tc ≃ 0.07 kelvin. First-order signatures of the transition weaken with increasing pressure, and we observe quantum critical scaling at the highest pressure, 2.4 gigapascals. Supported by model calculations, we suggest that these observations can be explained by a proximate DQCP inducing critical quantum fluctuations and emergent O(3) symmetry of the order parameters. Our findings offer a concrete experimental platform for investigation of the DQCP.

Quantum phase transition in NbN superconducting thin films

We systematically investigated the low-temperature transport properties of a series of NbN epitaxial films with thickness $t$ ranging from $\sim$2.0 to $\sim$4.0 nm. The films undergo a superconductor-insulator transition (SIT) with decreasing film thickness, and the critical sheet resistance for the SIT is close to the quantum resistance of Cooper pairs $h/4e^2$ (6.45 k$\Omega$). Besides the Berezinski-Koterlitz-Thouless transition, a magnetic-field-driven SIT is observed in those two-dimensional (2D) superconducting films (2.6 nm $\lesssim t \lesssim 4.0$ nm). Interestingly, it is found that the low-temperature magnetoresistance isotherms do not cross at a single fixed point but at a well-distinguished region for these superconducting films. The dynamical critical exponent obtained by analyzing these magnetoresistance isotherms is divergent as the quantum critical point is being approached. The behavior of the dynamical critical exponent, originating from quenched disorder at ultralow temperatures, provides direct evidence for the occurrence of quantum Griffiths singularity in the quantum phase transition process of the films. The field-driven anomalous metal (quantum metal) state does not appear in these films. Our results suggest that the quantum Griffiths singularity not only occurs in the highly crystalline 2D superconductors with superconductor-metal transition but also in those with SIT.

Strain-tuned quantum criticality in electronic Potts-nematic systems

Motivated by recent observations of threefold rotational symmetry breaking in twisted moir\'e systems, cold-atom optical lattices, quantum Hall systems, and triangular antiferromagnets, we phenomenologically investigate the strain-temperature phase diagram of the electronic 3-state Potts-nematic order. While in the absence of strain the quantum Potts-nematic transition is first order, quantum critical points (QCP) emerge when uniaxial strain is applied, whose nature depends on whether the strain is compressive or tensile. In one case, the nematic amplitude jumps between two nonzero values while the nematic director remains pinned, leading to a symmetry-preserving metanematic transition that terminates at a quantum critical end point. For the other type of strain, the nematic director unlocks from the strain direction and spontaneously breaks an in-plane twofold rotational symmetry, which in twisted moir\'e superlattices triggers an electric polarization. Such a piezoelectric transition changes from first to second order upon increasing strain, resulting in a quantum tricritical point. Using a Hertz-Millis approach, we show that these QCPs share interesting similarities with the widely studied Ising-nematic QCP. The existence of three minima in the nematic action also leaves fingerprints in the strain-nematic hysteresis curves, which display multiple loops. At nonzero temperatures, because the upper critical dimension of the 3-state Potts model is smaller than three, the Potts-nematic transition is expected to remain first order in three dimensions, but to change to second order in two dimensions (2D). As a result, the 2D strain-temperature phase diagram displays two first-order transition wings bounded by lines of critical end points or tricritical points, reminiscent of the phase diagram of metallic ferromagnets. We discuss how our results can be used to unambiguously identify spontaneous Potts-nematic order.

State space geometry of the spin-1 antiferromagnetic Heisenberg chain

We study the phase diagram of the spin-1 antiferromagnetic Heisenberg chain with uniaxial anisotropy and applied magnetic field in terms of the genuine multipartite entanglement as witnessed by the mean quantum Fisher information density. By considering the manifold generated by the staggered magnetization operator, we connect the state space curvature in the vicinity of the ground state of the Heisenberg chain to the genuine multipartite entanglement. Our analysis demonstrates that the quantum critical points and symmetry protected topological (SPT) phase exhibit large state space curvature, while the separable phases are completely flat, offering insight into the physical interpretation of state space curvature. We further show that the entanglement in the SPT phase is enhanced by the presence of uniaxial anisotropy and undiminished in the presence of uniform magnetic fields. The magnon condensate phase induced by large fields is shown to emanate from the Gaussian critical point and exhibits massive multipartite entanglement over a robust region of the parameter space.

Quantum criticality of a Z_{3}-symmetric spin chain with long-range interactions.

Based on large-scale density matrix renormalization group techniques, we investigate the critical behaviors of quantum three-state Potts chains with long-range interactions. Using fidelity susceptibility as an indicator, we obtain a complete phase diagram of the system. The results show that as the long-range interaction power α increases, the critical points f_{c}^{*} shift towards lower values. In addition, the critical threshold α_{c}(≈1.43) of the long-range interaction power is obtained for the first time by a nonperturbative numerical method. This indicates that the critical behavior of the system can be naturally divided into two distinct universality classes, namely the long-range (α<α_{c}) and short-range (α>α_{c}) universality classes, qualitatively consistent with the classical ϕ^{3} effective field theory. This work provides a useful reference for further research on phase transitions in quantum spin chains with long-range interaction.

Periodic Atomic Displacements and Visualization of the Electron-Lattice Interaction in the Cuprate

Traditionally, X-ray scattering techniques have been used to detect the breaking of the structural symmetry of the lattice, which accompanies a periodic displacement of the atoms associated with charge density wave (CDW) formation in the cuprate pseudogap states. Similarly, the Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM) has visualized the short-range CDW. However, local coupling of electrons to the lattice in the form of a short-range CDW has been a challenge to visualize, thus a link between these measurements has been missing. Here, we introduce a novel STM-based technique to visualize the local bond length variations obtained from topographic imaging with picometer precision. Application of this technique to the high-Tc cuprate superconductor Bi2Sr2CaCu2O8+{\delta} revealed a high-fidelity local lattice distortion of the BiO lattice as large as 2%. In addition, analysis of local breaking of rotational symmetry associated with the bond lengths reveals modulations around four-unit-cell periodicity in both B1 and E representations in the C4v group of the lattice, which coincides with the uni-directional d-symmetry CDW (dCDW) previously identified within the CuO2 planes, thus providing direct evidence of electron-lattice coupling in the pseudogap state and a link between the X-ray scattering and STM measurements. Overall, our results suggest that the periodic lattice displacements in E representations correspond to a locally-frozen version of the soft phonons identified by the X-ray scattering measurements, and a fluctuation of the bond length is reflected by the fluctuation of the dCDW formation near the quantum critical point.

A model of d-wave superconductivity, antiferromagnetism, and charge order on the square lattice

We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the hole-doped cuprates. The spin liquid can be described by a SU(2) gauge theory of Nf = 2 massless Dirac fermions carrying fundamental gauge charges-this is the low-energy theory of a mean-field state of fermionic spinons moving on the square lattice with π-flux per plaquette in the ℤ2 center of SU(2). This theory has an emergent SO(5)f global symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsion U at half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving in π ℤ2-flux. At half-filling, the low-energy theory of the Higgs sector has Nb = 2 relativistic bosons with a possible emergent SO(5)b global symmetry describing rotations between a d-wave superconductor, period-2 charge stripes, and the time-reversal breaking "d-density wave" state. We propose a conformal SU(2) gauge theory with Nf = 2 fundamental fermions, Nb = 2 fundamental bosons, and a SO(5)f×SO(5)b global symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5)f and a confining state which breaks SO(5)b. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order and d-wave superconductivity. A similar theory applies at nonzero doping and large U, with longer-range couplings of the chargons leading to charge order with longer periods.

Two superconducting states with broken time-reversal symmetry in FeSe1-xSx.

Iron-chalcogenide superconductors FeSe1-xSx possess unique electronic properties such as nonmagnetic nematic order and its quantum critical point. The nature of superconductivity with such nematicity is important for understanding the mechanism of unconventional superconductivity. A recent theory suggested the possible emergence of a fundamentally new class of superconductivity with the so-called Bogoliubov Fermi surfaces (BFSs) in this system. However, such an ultranodal pair state requires broken time-reversal symmetry (TRS) in the superconducting state, which has not been observed experimentally. Here, we report muon spin relaxation (μSR) measurements in FeSe1-xSx superconductors for 0 ≤ x ≤ 0.22 covering both orthorhombic (nematic) and tetragonal phases. We find that the zero-field muon relaxation rate is enhanced below the superconducting transition temperature Tc for all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transverse-field μSR measurements reveal that the superfluid density shows an unexpected and substantial reduction in the tetragonal phase (x > 0.17). This implies that a significant fraction of electrons remain unpaired in the zero-temperature limit, which cannot be explained by the known unconventional superconducting states with point or line nodes. The TRS breaking and the suppressed superfluid density in the tetragonal phase, together with the reported enhanced zero-energy excitations, are consistent with the ultranodal pair state with BFSs. The present results reveal two different superconducting states with broken TRS separated by the nematic critical point in FeSe1-xSx, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity.

Loop current fluctuations and quantum critical transport

We study electrical transport at quantum critical points (QCPs) associated with loop current ordering in a metal, focusing specifically on models of the “Hertz-Millis” type. At the infrared (IR) fixed point and in the absence of disorder, the simplest such models have infinite DC conductivity and zero incoherent conductivity at nonzero frequencies. However, we find that a particular deformation, involving NN species of bosons and fermions with random couplings in flavor space, admits a finite incoherent, frequency-dependent conductivity at the IR fixed point, \sigma(\omega&amp;gt;0)\sim\omega^{-2/z}σ(ω&gt;0)∼ω−2/z, where zz is the boson dynamical exponent. Leveraging the non-perturbative structure of quantum anomalies, we develop a powerful calculational method for transport. The resulting "anomaly-assisted large NN expansion" allows us to extract the conductivity systematically. Although our results imply that such random-flavor models are problematic as a description of the physical N = 1N=1 system, they serve to illustrate some general conditions for quantum critical transport as well as the anomaly-assisted calculational methods. In addition, we revisit an old result that irrelevant operators generate a frequency-dependent conductivity, \sigma(\omega&amp;gt;0) \sim \omega^{-2(z-2)/z}σ(ω&gt;0)∼ω−2(z−2)/z, in problems of this kind. We show explicitly, within the scope of the original calculation, that this result does not hold for any order parameter.

Effects of V concentration on the physical properties of Cr1−x Al x alloy system

Electrical resistivity (ρ), magnetic susceptibility (χ) and thermoelectric power (S) studies reported previously on the (Cr1-x Al x )99V1 alloy system indicate a suppression of antiferromagnetism in the concentration range 0.015 ≤ x ≤ 0.040. The present study incorporates Sommerfeld electronic specific heat coefficient (γ), thermal conductivity (κ), Hall coefficient (R H) and analyses of the previous results in order to have a comprehensive study of the alloy system. γ(x) depicts two peaks close to the same concentrations where dS/dT|T→2K(x) have minima, i.e. at x c1 ≈ 0.015 and x c2 ≈ 0.040. Such peaks and minima, respectively, have been considered as key signatures of quantum criticality (QC) in alloys of Cr. Evidence of band structure modification in the alloy system is shown by a change of slope in the Nordheim-Gorter (N-G) relationship showing a minimum at an extrapolated concentration x = 0.035. The slope is positive for the incommensurate (I) spin-density-wave (SDW) alloys with x < 0.035 and a negative for the commensurate (C) SDW alloys with x > 0.035. A behaviour reminiscent of changes in the band structure is also observed in the Lorenz number, L(x), for the alloy with x = 0. R H(T) results in the range 0 ≤ x ≤ 0.026 have a sharp increase in the charge carrier density, n 2K = [qR H(2k)]−1, at the ISDW to paramagnetic (P) phase transition. The concentrations x = 0.015 and x = 0.040 are therefore considered ISDW to P and P to CSDW quantum critical points, respectively.