Quantum Critical Research Articles

Exact Fisher zeros and thermofield dynamics across a quantum critical point

Exact Fisher zeros and thermofield dynamics across a quantum critical point

Transport phase diagram and anomalous metallicity in superconducting infinite-layer nickelates.

Despite obvious similarities in their electronic and crystallographic structures, it remains unclear whether the interactions that shape the normal and superconducting (SC) state properties of high-Tc cuprates and infinite-layer nickelates (ILNs) have the same origin. This question has been brought into sharper focus with recent studies on ILNs of improved crystallinity that reveal a SC dome of comparable extent and similar transport properties above Tc as the hole-doped cuprates. The evolution of these properties in the magnetic-field-induced normal state, however, has yet to be determined. Here, we examine the magnetotransport properties of new-generation Nd1-xSrxNiO2 films in the T→0 limit across the phase diagram in fields up to 54 T. This extensive study reveals that the limiting low-T form of the normal-state resistivity in ILNs exhibits non-Fermi-liquid behaviour over an extended doping range inside the SC dome, rather than at a singular quantum critical point. While there are clear differences in the charge dynamics of ILNs and cuprates, most notably in the magnetoresistance, our findings reveal that both systems exhibit anomalous metallicity characteristic of a quantum critical phase.

Highly anisotropic superconducting gap near the nematic quantum critical point of FeSe1−xSx

Highly anisotropic superconducting gap near the nematic quantum critical point of FeSe1−xSx

Multipartite entanglement in crossing the quantum critical point

Abstract We investigate the multipartite entanglement for a slow quantum quench crossing a critical point. We consider the quantum Ising model and the Lipkin-Meshkov-Glick model, which are local and full-connected quantum systems, respectively. The multipartite entanglement is quantified by quantum Fisher information with the generator defined as the operator of the ferromagnetic order parameter. The quench dynamics begins with a ground state in a paramagnetic phase, and then the transverse field is driven slowly to cross a quantum critical point, and ends with a zero transverse field. For the quantum Ising model, based on methods of matrix product states, we calculate the quantum Fisher information density of the final state. Numerical results of both linear and nonlinear quenches show that the quantum Fisher information density of the final state scales as a power law of the quench rate, which overall conforms to the prediction of the Kibble-Zurek mechanism with a small correction. We show that this correction results from the long-range behaviors. We also calculate the quantum Fisher information density in the Lipkin-Meshkov-Glick model. The results show that the scaling of quantum Fisher information in this full-connected system conforms to the Kibble-Zurek mechanism better, since the long-range physics cannot be defined in this nonlocal system. Our results reveal that the multipartite entanglement provides an alternative viewpoint to understand the dynamics of quantum phase transitions, specifically, the nontrivial long-range physics.

Crystal growth and pressure effect on the transport properties in 122-type (La,Na,K)Fe2As2 superconductors

Abstract High-quality single crystals are essential for probing the intrinsic properties of unconventional superconductors. In this work, we report the successful growth of (La,Na,K)Fe2As2 single crystals, a novel 122-type iron-based superconductor, using the self-flux method. The crystal structure and chemical composition were characterized through x-ray diffraction and energy-dispersive x-ray spectroscopy. The (La,Na,K)Fe2As2 single crystals exhibit bulk superconductivity, with a critical transition temperature Tc of approximately 22 K. Magnetization measurements reveal a second peak effect and a critical current density Jc ~ 5×105 A/cm2 at 2 K in a self-field. The upper critical field anisotropy was systematically studied within the framework of the anisotropic Ginzburg–Landau theory, yielding an anisotropy value of approximately 2.6. Furthermore, we employ the diamond anvil cell technique to investigate the pressure effect on (La,Na,K)Fe2As2. Our results demonstrate that superconductivity is gradually suppressed with increasing pressure, while the normal state resistivity at low temperatures evolves from non-Fermi liquid to Fermi liquid behavior. This observation suggests that (La,Na,K)Fe2As2 may be situated on the right of the quantum critical point or, at the very least, within the over-doped region. These findings provide a critical sample platform and experimental insights for advancing the understanding of the physical properties of the newly discovered (La,Na,K)Fe2As2 superconductors.

Emergent Properties of the Periodic Anderson Model: A High-Resolution, Real-Frequency Study of Heavy-Fermion Quantum Criticality

We study paramagnetic quantum criticality in the periodic Anderson model (PAM) using cellular dynamical mean-field theory (CDMFT), with the numerical renormalization group (NRG) as a cluster impurity solver. The PAM describes itinerant c electrons hybridizing with a lattice of localized f electrons. At zero temperature, it exhibits a much-studied quantum phase transition from a Kondo phase to a Ruderman-Kittel-Kasuya-Yosida (RKKY) phase when the hybridization is decreased through a so-called Kondo breakdown quantum critical point (KB QCP). There, Kondo screening of f spins by c electrons breaks down, so that f excitations change their character from somewhat itinerant to mainly localized, while c excitations remain itinerant. Building on , which interpreted the KB transition as an orbital-selective Mott transition, we here elucidate its nature in great detail by performing a high-resolution, real-frequency study of various dynamical quantities (susceptibilities, self-energies, and spectral functions). NRG allows us to study the quantum critical regime governed by the QCP and located between two temperature scales, TFL<TNFL. In this regime, we find fingerprints of non-Fermi-liquid (NFL) behavior in several dynamical susceptibilities. Surprisingly, CDMFT self-consistency is essential to stabilize the QCP and the NFL regime. The Fermi-liquid (FL) scale TFL decreases toward and vanishes at the KB QCP; at temperatures below TFL, FL behavior emerges. At T=0, we find the following properties. The KB transition is continuous. The f quasiparticle weight decreases continuously as the transition is approached from either side, vanishing only at the KB QCP. Therefore, the quasiparticle weight of the f band is nonzero not only in the Kondo phase, but also in the RKKY phase; hence, the FL quasiparticles comprise c f electrons in both phases. The Fermi surface (FS) volumes in the two phases differ, implying a FS reconstruction at the KB QCP. Whereas the large-FS Kondo phase has a two-band structure as expected, the small-FS RKKY phase unexpectedly has a three-band structure. We provide a detailed analysis of quasiparticle properties of both the Kondo and, for the first time, also the RKKY phase and uncover their differences. The FS reconstruction is accompanied by the appearance of a Luttinger surface on which the f self-energy diverges. The volumes of the Luttinger and Fermi surfaces are related to the charge density by a generalized Luttinger sum rule. We interpret the small FS volume and the emergent Luttinger surface as evidence for f-electron fractionalization in the RKKY phase. Finally, we compute the temperature dependence of the Hall coefficient and the specific heat, finding good qualitative agreement with experiments. Published by the American Physical Society 2024

Quantum steering ellipsoids and quantum obesity in critical systems

Abstract Quantum obesity (QO) is a novel function introduced to quantify quantum correlations that go beyond traditional measures like entanglement, while also functioning as an entanglement witness. One of the key strengths of QO lies in its analyticity for arbitrary states of bipartite systems, making it a more accessible and versatile tool compared to other measures of quantum correlations, such as quantum discord. In this work, we highlight the importance of QO as a fundamental quantity for identifying signatures of quantum phase transitions, which are critical changes in the ground state of quantum systems driven by quantum fluctuations. We introduce a mechanism based on local filtering operations designed to enhance the critical behavior of QO near phase transition points, providing a deeper understanding of these phenomena. Furthermore, we present a theorem that characterizes how QO transforms under local quantum operations and classical communications (LOCC), which broadens its applicability to a wider range of quantum systems. This opens new avenues for exploring quantum criticality and other novel quantum phenomena by leveraging the analytically computable, pairwise QO, thus offering both theoretical insights and practical applications in quantum information science.

High-Resolution Spectroscopy of the Intermediate Impurity States near a Quantum Phase Transition.

The intermediate behavior near a quantum phase transition is crucial for understanding the quantum criticality of various competing phases and their separate origins, yet it remains unexplored for the multiple Yu-Shiba-Rusinov (YSR) states. Here, we investigated the detailed spectroscopic change of the exchange-coupling-dependent YSR states near a quantum phase transition. The initially developed one pair of YSR states, induced by the Fe vacancy in monolayer Fe(Te,Se) superconductor, are clearly resolved with high resolution showing an evolution into two pairs of YSR peaks yet with dichotomy in their spectral features as they enter the quantum phase transition region. Spectral-weight analysis suggests that the double YSR pairs occur as a result of field splitting by the magnetic anisotropy. Our findings unveil the intermediate region of a quantum phase transition with a magnetic anisotropy-induced splitting of the YSR resonance, and highlight a prospect for developing functional electronics based on the flexibly controllable multiple quantum states.

Strange Metal and Superconductor in the Two-Dimensional Yukawa-Sachdev-Ye-Kitaev Model.

The two-dimensional Yukawa-Sachdev-Ye-Kitaev (2D-YSYK) model provides a universal theory of quantum phase transitions in metals in the presence of quenched random spatial fluctuations in the local position of the quantum critical point. It has a Fermi surface coupled to a scalar field by spatially random Yukawa interactions. We present full numerical solutions of a self-consistent disorder averaged analysis of the 2D-YSYK model in both the normal and superconducting states, obtaining electronic spectral functions, frequency-dependent conductivity, and superfluid stiffness. Our results reproduce key aspects of observations in the cuprates as analyzed by Michon etal. [Nat. Commun. 14, 3033 (2023)NCAOBW2041-172310.1038/s41467-023-38762-5]. We also find a regime of increasing zero temperature superfluid stiffness with decreasing superconducting critical temperature, as is observed in bulk cuprates.

Fractional Chern Insulators in Twisted Bilayer MoTe_{2}: A Composite Fermion Perspective.

The discovery of fractional Chern insulators (FCIs) in twisted bilayer MoTe_{2} has sparked significant interest in fractional topological matter without external magnetic fields. Unlike the flat dispersion of Landau levels, moiré electronic states are influenced by lattice effects within a nanometer-scale superlattice. This Letter examines the impact of these lattice effects on the topological phases in twisted bilayer MoTe_{2}, uncovering a family of FCIs with Abelian anyonic quasiparticles. Using a composite fermion approach, we identify a sequence of FCIs with fractional Hall conductivities σ_{xy}=[C/(2C+1)](e^{2}/h) linked to partial filling ν_{h} of holes of the topmost moiré valence band. These states emerge from incompressible composite fermion bands of Chern number C within a complex Hofstadter spectrum. This approach explains FCIs with Hall conductivities σ_{xy}=(2/3)e^{2}/h and σ_{xy}=(3/5)e^{2}/h at fractional fillings ν_{h}=2/3 and ν_{h}=3/5 observed in experiments, and uncovers other fractal FCI states. The Hofstadter spectrum reveals new phenomena, distinct from Landau levels, including a higher-order Van Hove singularity (HOVHS) at half-filling, leading to novel quantum phase transitions. This Letter offers a comprehensive framework for understanding FCIs in transition metal dichalcogenide moiré systems and highlights mechanisms for topological quantum criticality.

Cavity-magnon-polariton spectroscopy of strongly hybridized electro-nuclear spin excitations in LiHoF4

We first present a formalism that incorporates the input-output formalism and the linear response theory to employ cavity-magnon-polariton coupling as a spectroscopic tool for investigating strongly hybridized electro-nuclear spin excitations. A microscopic relation between the generalized susceptibility and the scattering parameter |S11|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|S_{11}|$$\\end{document} in strongly hybridized cavity-magnon-polariton systems has been derived without resorting to semi-classical approximations. The formalism is then applied to both analyze and simulate a specific systems comprising a model quantum Ising magnet (LiHoF4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiHoF}_4$$\\end{document}) and a high-finesse 3D re-entrant cavity resonator. Quantitative information on the electro-nuclear spin states in LiHoF4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiHoF}_4$$\\end{document} is extracted, and the experimental observations across a broad parameter range were numerically reproduced, including an external magnetic field traversing a quantum critical point. The method potentially opens a new avenue not only for further studies on the quantum phase transition in LiHoF4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiHoF}_4$$\\end{document} but also for a wide range of complex magnetic systems.

Multipartite nonlocality spectrum and quantum criticality in one-dimensional quantum chains

Multipartite nonlocality spectrum and quantum criticality in one-dimensional quantum chains

Quantum-coherence-assisted dynamical phase transition in the one-dimensional transverse-field Ising model

Quantum coherence will undoubtedly play a fundamental role in understanding the dynamics of quantum many-body systems; therefore, to be able to reveal its genuine contribution is of great importance. In this paper, we focus our discussions on the one-dimensional transverse field quantum Ising model initialized in the coherent Gibbs state, and investigate the effects of quantum coherence on dynamical quantum phase transition (DQPT). After quenching the strength of the transverse field, the effects of quantum coherence are studied using Fisher zeros and the rate function of the Loschmidt echo. We find that quantum coherence not only recovers DQPT destroyed by thermal fluctuations, but also generates some entirely new DQPTs, which are independent of the equilibrium quantum critical point. We also find that the Fisher zero cutting the imaginary axis is not sufficient to generate DQPT because it also requires the Fisher zeros to be tightly bound close enough to the neighborhood of the imaginary axis. It can be manifested that DQPTs are rooted in quantum fluctuations. This work reveals new information on the fundamental connection between quantum critical phenomena and quantum coherence.

Entanglement Entropy and Deconfined Criticality: Emergent SO(5) Symmetry and Proper Lattice Bipartition.

We study the Rényi entanglement entropy (EE) of the two-dimensional J-Q model, the emblematic quantum spin model of deconfined criticality at the phase transition between antiferromagnetic and valence-bond-solid ground states. State-of-the-art quantum MonteCarlo calculations of the EE reveal critical corner contributions that scale logarithmically with the system size, with a coefficient in remarkable agreement with the form expected from a large-N conformal field theory with SO(N=5) symmetry. However, details of the bipartition of the lattice are crucial in order to observe this behavior. If the subsystem for the reduced density matrix does not properly accommodate valence-bond fluctuations, logarithmic contributions appear even for cornerless bipartitions. We here use a 45° tilted cut on the square lattice. Beyond supporting an SO(5) deconfined quantum critical point, our results for both the regular and tilted cuts demonstrate important microscopic aspects of the EE that are not captured by conformal field theory.

Anomalous lattice contraction and emerging topological phases in Bi-substituted Sm2Ir2O7

We demonstrate that substituting Bi for Sm in the pyrochlore Sm$_2$Ir$_2$O$_7$ induces an anomalous lattice contraction, with $\Delta a \sim -0.012$~\AA~observed at 10\% Bi substitution, where 'a' denotes the lattice constant. Beyond 10\% Bi substitution, the lattice expands according to Vegard's law. Within this anomalous substitution range, the resistivity shows a 1/T behavior up to 2\% Bi-substitution, while near 10\% substitution a -lnT dependence is observed. These resistivity behaviors suggest the possibility of a Weyl phase up to 2\% Bi substitution, which transforms to a semimetallic quadratic band touching (QBT) topological phase near 10\%. For the intermediate composition (Sm$_{0.95}$Bi$_{0.05}$)$_2$Ir$_2$O$_7$, the resistivity scales as $\rm 1/T^{1/4}$, possibly due to its proximity to a proposed quantum critical point at the Weyl-QBT phase boundary [Phys. Rev. X 4, 041027 (2014)]. The samples were characterized using synchrotron powder X-ray diffraction, X-ray near-edge fine structure (XANES), and Extended X-ray absorption fine structure (EXAFS) probes. Additionally, magnetic susceptibility and heat capacity measurements were conducted to provide further support.

Strange-metal behavior without fine tuning in PrV2Al20

Strange-metal behavior observed in the praseodymium-based heavy-fermion material PrV2Al20 has been tentatively interpreted in the framework of proximity to a quantum critical point (QCP) associated with quadrupolar ordering. Here, we demonstrate that an alternative, natural explanation exists without invoking a QCP, in terms of the unconventional nature of the quadrupolar Kondo effect taking place in non-Kramers ions. Using a combination of density-functional theory calculations and analytical arguments, we construct a periodic Anderson model with realistic parameters to describe PrV2Al20. We solve the model using dynamical mean-field theory preserving the model symmetries and demonstrate the non-Fermi liquid strange-metal behavior stemming from the two-channel nature of the quadrupolar Kondo effect. Our calculations provide an explanation for the puzzling temperature dependence in the magnetic susceptibility and provide a basis for analyzing future photoemission experiments. Published by the American Physical Society 2024

Construction of superconducting dome and emergence of quantum critical region in holography

In this work, we investigate an extended model of holographic superconductor by a nonlinear electrodynamic interaction coupled to a complex scalar field. This nonlinear interaction term can make a quantum phase transition at zero temperature with finite charge carrier density. By solving full equations of motion, we can construct various shapes of the superconducting phase in the phase diagram. With a specific choice of interaction coefficients, we can construct a phase diagram with a superconducting dome. Also, we find a new geometric solution inside the superconducting dome, which turns out to be a Lifshitz-type geometry. This geometry is characterized by a dynamical critical exponent, which plays a crucial role near the quantum critical point. We refer to this region of the phase diagram as a quantum critical region. Published by the American Physical Society 2024

Charge order near the antiferromagnetic quantum critical point in the trilayer high Tc cuprate HgBa2Ca2Cu3O8+δ

We study the transport properties of underdoped trilayer cuprate HgBa2Ca2Cu3O8+δ with doping level p = 0.10–0.12 in magnetic field up to 88 T. We report for the first time in a cuprate superconductor a dramatic change of the quantum oscillation spectrum versus temperature, which is accompanied by a sign change of the Hall effect below T ≈10 K. Based on numerical simulations, we infer a Fermi surface reconstruction in the inner plane from an antiferromagnetic state (hole pockets) to a biaxial charge density wave state (electron pockets). We show that both orders compete and share the same hotspots of the Fermi surface, and we discuss our result in the context of spin-fermion models.

Exact results of the one-dimensional repulsive Hubbard model

We present analytical results of the fundamental properties of the one-dimensional (1D) Hubbard model with a repulsive interaction. The new model results with arbitrary external fields include: (I) using the exact solutions of the Bethe ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. We then investigate the gapped excitations in terms of the spin string and thek-Λstring bound states at arbitrary driving fields, showing subtle differences in spin magnons and chargeη-pair excitations. (II) For a high-density and high spin magnetization region, i.e. near the quadruple critical point, we further analytically obtain the thermodynamic properties, dimensionless ratios and scaling functions near quantum phase transitions. (III) Importantly, we give the general scaling functions at quantum criticality for arbitrary filling and interaction strength. These can directly apply to other integrable models. (IV) Based on the fractional excitations and the scaling laws, the spin-incoherent Luttinger liquid (SILL) with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of conformal field theory. We also, for the first time, obtain the analytical results of the thermodynamics for the SILL. (V) Finally, to capture deeper insights into the Mott insulator and interaction-driven criticality, we further study the double occupancy and propose its associated contact and contact susceptibilities, through which an adiabatic cooling scheme based upon quantum criticality is proposed. In this scenario, we build up general relations among arbitrary external- and internal-potential-driven quantum phase transitions, providing a comprehensive understanding of quantum criticality. Our methods offer rich perspectives of quantum integrability and offer promising guidance for future experiments with interacting electrons and ultracold atoms, both with and without a lattice.

Field-Induced Quantum Criticality in Two-Coupled Two-Leg Heisenberg Ladders

We use the bond mean field theory, which is based on the Jordan–Wigner fermionization, to investigate the quantum critical behavior of a system composed of two-coupled Heisenberg Spin-[Formula: see text] two-leg ladders in the presence of an applied magnetic field. By examining the dependence of the ground state on the magnetic field for different coupling constants, we investigate the field-induced quantum criticality. The magnetization exhibits distinct plateaus: a zero magnetization plateau for fields below a threshold value of the field [Formula: see text] and a saturation plateau for fields exceeding a second critical value [Formula: see text]. The spin bond parameters are calculated and found to show a critical behavior at [Formula: see text].