Signature Of Quantum Phase Transition Research Articles

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.

Relaxation dynamics in the alternating XY chain following a quantum quench

We investigate the relaxation dynamics of the fermion two-point correlation function Cmn(t)=〈ψ(t)∣cm†cn∣ψ(t)〉 in the XY chain with alternating nearest-neighbor hopping interaction after a quench. We find that the deviation δ C mn (t) = C mn (t) − C mn (∞) decays with time following the power law behavior t −μ , where the exponent μ depends on whether the quench is to the commensurate phase (μ = 1) or incommensurate phase ( μ=12 ). This decay of δ C mn (t) arises from the transient behavior of the double-excited quasiparticle occupations and the transitions between different excitation spectra. Furthermore, we find that the steady value C mn (∞) only involves the average fermion occupation numbers (i.e. the average excited single particle) over the time-evolved state, which are different from the ground state expectation values. We also observe nonanalytic singularities in the steady value C mn (∞) for the quench to the critical points of the quantum phase transitions (QPTs), suggesting its potential use as a signature of QPTs.

Signatures of Dissipation Driven Quantum Phase Transition in Rabi Model.

By using the worldline MonteCarlo technique, matrix product state, and a variational approach àla Feynman, we investigate the equilibrium properties and relaxation features of the dissipative quantum Rabi model, where a two level system is coupled to a linear harmonic oscillator embedded in a viscous fluid. We show that, in the Ohmic regime, a Beretzinski-Kosterlitz-Thouless quantum phase transition occurs by varying the coupling strength between the two level system and the oscillator. This is a nonperturbative result, occurring even for extremely low dissipation magnitude. By using state-of-the-art theoretical methods, we unveil the features of the relaxation towards the thermodynamic equilibrium, pointing out the signatures of quantum phase transition both in the time and frequency domains. We prove that, for low and moderate values of the dissipation, the quantum phase transition occurs in the deep strong coupling regime. We propose to realize this model by coupling a flux qubit and a damped LC oscillator.

High-harmonic spectroscopy of quantum phase transitions in a high-Tc superconductor

We report on the nonlinear optical signatures of quantum phase transitions in the high-temperature superconductor YBCO, observed through high harmonic generation. While the linear optical response of the material is largely unchanged when cooling across the phase transitions, the nonlinear optical response sensitively imprints two critical points, one at the critical temperature of the cuprate with the exponential growth of the surface harmonic yield in the superconducting phase and another critical point, which marks the transition from strange metal to pseudogap phase. To reveal the underlying microscopic quantum dynamics, a strong-field quasi-Hubbard model was developed, which describes the measured optical response dependent on the formation of Cooper pairs. Further, the theory provides insight into the carrier scattering dynamics and allows us to differentiate between the superconducting, pseudogap, and strange metal phases. The direct connection between nonlinear optical response and microscopic dynamics provides a powerful methodology to study quantum phase transitions in correlated materials. Further implications are light wave control over intricate quantum phases, light-matter hybrids, and application for optical quantum computing.

Signatures of Quantum Phase Transitions after Quenches in Quantum Chaotic One-Dimensional Systems

Quantum phase transitions are central to our understanding of why matter at very low temperatures can exhibit starkly different properties upon small changes of microscopic parameters. Accurately locating those transitions is challenging experimentally and theoretically. Here, we show that the antithetic strategy of forcing systems out of equilibrium via sudden quenches provides a route to locate quantum phase transitions. Specifically, we show that such transitions imprint distinctive features in the intermediate-time dynamics, and results after equilibration, of local observables in quantum chaotic spin chains. Furthermore, we show that the effective temperature in the expected thermal-like states after equilibration can exhibit minima in the vicinity of the quantum critical points. We discuss how to test our results in experiments with Rydberg atoms and explore nonequilibrium signatures of quantum critical points in models with topological transitions.7 MoreReceived 10 April 2020Revised 10 May 2021Accepted 13 July 2021DOI:https://doi.org/10.1103/PhysRevX.11.031062Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium statistical mechanicsQuantum phase transitionsQuantum quenchQuantum statistical mechanicsCondensed Matter, Materials & Applied PhysicsStatistical Physics

Quantum phase diagrams of matter-field Hamiltonians II: Wigner function analysis

Non-classical states are of practical interest in quantum computing and quantum metrology. These states can be detected through their Wigner function negativity in some regions. We show that the surfaces of minimum fidelity or maximum Bures distance constitute a signature of quantum phase transitions. Additionally the behaviour of the Wigner function associated to the field modes carry the information of both, the entanglement properties between matter and field sectors, and the regions of the parameter space where the quantum phase transitions take place. A finer classification for the continuous phase transitions is obtained through the computation of the surface of maximum Bures distance.

Critical stability and quantum phase transition of two-electron system under exponential-cosine-screened-Coulomb interaction

The stability of two electron system under the influence of the exponential-cosine-screened-Coulomb (ECSC) potential has been studied as a function of continuously varying nuclear charge (Z) and screening constant (μ). Inter-electronic correlation has explicitly been considered by adopting Hylleraas type basis set under Ritz variational framework. The correlated basis integrals originating from the elements of Hamiltonian and overlap matrices are evaluated analytically. Critical nuclear charges (Zc), the minimum amount of nuclear charge required to form at least one bound state, corresponding to different μ values have been predicted. Different structural properties along with two-particle densities (TPD) for all possible orientations of the electrons have been estimated using the optimized wave function. Prominent signature of quantum phase transition (QPT) of the system around the Zc values has been reported. A comparative study has been done on the critical stability of the system under the influence of ECSC potential, screened Coulomb (SC) potential and pure Coulomb (PC) potential.

Rényi entanglement entropy of Fermi and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories

We present a new method for calculating Renyi entanglement entropies for fermionic field-theories originating from microscopic Hamiltonians. The method builds on an operator identity which we discover for the first time. The identity leads to the representation of traces of operator products, and thus Renyi entropies of a subsystem, in terms of fermionic-displacement operators. This allows for a very transparent path-integral formulation, both in and out-of-equilibrium, having a simple boundary condition on the fermionic fields. The method is validated by reproducing well known expressions for entanglement entropy in terms of the correlation matrix for non-interacting fermions. We demonstrate the effectiveness of the method by explicitly formulating the field theory for Renyi entropy in a few zero and higher-dimensional large-$N$ interacting models based on the Sachdev-Ye-Kitaev (SYK) model, and for the Hubbard model within dynamical mean-field theory (DMFT) approximation. We use the formulation to compute Renyi entanglement entropy of interacting Fermi liquid (FL) and non-Fermi liquid (NFL) states in the large-$N$ models and compare successfully with the results obtained via exact diagonalization for finite $N$. We elucidate the connection between entanglement entropy and residual entropy of the NFL ground state in the SYK model and extract sharp signatures of quantum phase transition in the entanglement entropy across an NFL to FL transition. Furthermore, we employ the method to obtain nontrivial system-size scaling of entanglement in an interacting diffusive metal described by a chain of SYK dots.

Classical and Quantum Signatures of Quantum Phase Transitions in a (Pseudo) Relativistic Many-Body System

We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in attractive one-dimensional bosonic gases. In this new scenario, due to the simultaneous existence of the linear dispersion and the bosonic nature of the system, special care must be taken with the choice of energy region where the transition takes place. Still, due to a crucial adiabatic separation of scales, and identified through extensive numerical diagonalization, a suitable effective model describing the transition is found. The corresponding mean-field analysis based on this effective model provides accurate predictions for the location of the quantum phase transition when compared against extensive numerical simulations. Furthermore, we numerically investigate the dynamical exponents characterizing the approach from its finite-size precursors to the sharp quantum phase transition in the thermodynamic limit.

Steered quantum coherence as a signature of quantum phase transitions in spin chains

We propose to use the steered quantum coherence (SQC) as a signature of quantum phase transitions (QPTs). By considering various spin chain models, including the transverse-field Ising model, \textit{XY} model, and \textit{XX} model with three-spin interaction, we showed that the SQC and its first-order derivative succeed in signaling different critical points of QPTs. In particular, the SQC method is effective for any spin pair chosen from the chain, and the strength of SQC, in contrast to entanglement and quantum discord, is insensitive to the distance (provided it is not very short) of the tested spins, which makes it convenient for practical use as there is no need for careful choice of two spins in the chain.

Critical stability and quantum phase transition of screened two‐electron system

AbstractThe ground state energy and structural properties of a model two‐electron system (Zee), bound via screened Coulomb interaction with nuclear charge Z, have been studied under the variational framework. Hylleraas type basis has been adopted for explicit incorporation of the electron–electron correlation. Critical nuclear charges (Zc) of Zee system have been reported for different screening parameters (μ). Expectation values of different structural properties have been estimated to predict the internal structure of the Zee system. The variation of the structural properties with respect to Z for different μ reveals the signature of quantum phase transition (QPT) in the vicinity of Zc. Moreover, the nature of variation of these properties with respect to Z in case of bare Coulomb or free system (μ = 0) is completely opposite to those of screened system (μ ≠ 0). Radial two‐particle density (TPD) confirms the symmetry breaking of the electronic structure and therefore QPT in the vicinity of Zc.

Quantum Renormalization of Spin Squeezing in Spin Chains

By employing quantum renormalization group (QRG) method, we investigate quantum phase transitions (QPT) in the Ising transverse field (ITF) model and in the XXZ Heisenberg model, with and without Dzyaloshinskii Moriya (DM) interaction, on a periodic chain of N lattice sites. We adopt a new approach called spin squeezing as an indicator of QPT. Spin squeezing, through analytical expression of a spin squeezing parameter, is calculated after each step of QRG. As the scale of the system becomes larger, (after many QRG steps), the ground state (GS) spin squeezing parameters show an abrupt change at a quantum critical point (QCP). Moreover, in all of the studied models, the first derivative of the spin squeezing parameter with respect to the control parameter is discontinuous, which is a signature of QPT. The spin squeezing parameters develop their saturated values after enough QRG iterations. The divergence exponent of the first derivative of the spin squeezing parameter in the near vicinity of the QCP is associated with the critical exponent of the correlation length.

Signatures of quantum phase transitions from the boundary of the numerical range

The ground state energy of a finite-dimensional one-parameter Hamiltonian and the continuity of a maximum-entropy inference map are discussed in the context of quantum critical phenomena. The domain of the inference map is a convex compact set in the plane, called the numerical range. We study the differential geometry of its boundary in relation to the ground state energy. We prove that discontinuities of the inference map correspond to $C^1$-smooth crossings of the ground state energy with a higher energy level. Discontinuities may appear only at $C^1$-smooth points of the boundary of the numerical range considered as a manifold. Discontinuities exist at all $C^2$-smooth non-analytic boundary points and are essentially stronger than at analytic points or at points which are merely $C^1$-smooth (non-exposed points).

Well-Known Distinctive Signatures of Quantum Phase Transition in Shape Coexistence Configuration of Nuclei

It is interesting that a change of nuclear shape may be described in terms of a phase transition. This paper studies the quantum phase transition of the U(5) to SO(6) in the interacting boson model (IBM) on the finite number N of bosons. This paper explores the well-known distinctive signatures of transition from spherical vibrational to γ-soft shape phase in the IBM with the variation of a control parameter. Quantum phase transitions occur as a result of properties of ground and excited states levels. We apply an affine $\widehat {SU(1,1)}$ approach to numerically solve non-linear Bethe Ansatz equation and point out what observables are particularly sensitive to the transition. The main aim of this work is to describe the most prominent observables of QPT by using IBM in shape coexistence configuration. We calculate energies of excited states and signatures of QPT as energy surface, energy ratio, energy differences, quadrupole electric transition rates and expectation values of boson number operators and show their behavior in QPT. These observables are calculated and examined for 98 − 102Mo isotopes.

Large bond-dimension time-evolution block decimation study of the XXZ quantum spin chains of S = 1/2 and 1

We study quantum phase transitions of a XXZ spin model with spin S = 1/2 and 1 in one dimension. The XXZ spin chain is one of basic models in understanding various one-dimensional magnetic materials. To study this model, we construct infinite-lattice matrix product state (iMPS), which is a tensor product form for a one-dimensional many-body quantum wave function. By using timeevolution- block-decimation method (TEBD) on iMPS, we obtain the ground states of the XXZ model at zero temperature. This method is very delicate in calculating ground states so that we developed a reliable method of finding the ground state with the dimension of entanglement coefficients up to 300, which is beyond the previous works. By analyzing ground-state energies, half-chain entanglement entropies, and entanglement spectrum, we found the signatures of quantum phase transitions between ferromagnetic phase, XY phase, Haldane phase, and antiferromagnetic phase.

Quantum phase transitions in Ba(1−x)CaxFe12O19 ( 0≤x≤0.10 )

The ground state of BaFe12O19 (BFO) is controversial as three different quantum states, namely quantum paraelectric, frustrated antiferroelectric and quantum electric dipole liquid (QEDL), have been proposed. We have investigated the quantum critical behavior of BFO as a function of chemical pressure (a non-thermal variable) generated by smaller isovalent ion Ca2+ at the Ba2+ site. Analysis of synchrotron x-ray diffraction data confirms that Ca2+ substitution generates positive chemical pressure. Our dielectric measurements reveal that Ca2+ substitution drives BFO away from its quantum critical point (QCP) and stabilizes a quantum electric dipolar glass state whose dielectric peak temperature (Tc) increases with increasing Ca2+ content as Tc ~ (x-xc)1/2, a canonical signature of quantum phase transitions. Our dielectric measurements reveal that pure BFO is slightly away from its QCP with a Tc of 2.91 K. Specific heat measurements reveal excess specific heat of non-Debye and non-magnetic origin with linear temperature dependence below Tc which could be due to QEDL state of BFO.

Quantum correlation dynamics subjected to critical spin environment with short-range anisotropic interaction.

Short-range interaction among the spins can not only results in the rich phase diagram but also brings about fascinating phenomenon both in the contexts of quantum computing and information. In this paper, we investigate the quantum correlation of the system coupled to a surrounding environment with short-range anisotropic interaction. It is shown that the decay of quantum correlation of the central spins measured by pairwise entanglement and quantum discord can serve as a signature of quantum phase transition. In addition, we study the decoherence factor of the system when the environment is in the vicinity of the phase transition point. In the strong coupling regime, the decay of the decoherence factor exhibits Gaussian envelop in the time domain. However, in weak coupling limit, the quantum correlation of the system is robust against the disturbance of the magnetic field through optimal control of the anisotropic short-range interaction strength. Based on this, the effects of the short-range anisotropic interaction on the sudden transition from classical to quantum decoherence are also presented.

Semiclassical excited-state signatures of quantum phase transitions in spin chains with variable-range interactions

We study the excitation spectrum of a family of transverse-field spin chain models with variable interaction range and arbitrary spin $S$, which in the case of $S=1/2$ interpolates between the Lipkin-Meshkov-Glick and the Ising model. For any finite number $N$ of spins, a semiclassical energy manifold is derived in the large-$S$ limit employing bosonization methods, and its geometry is shown to determine not only the leading-order term but also the higher-order quantum fluctuations. Based on a multi-configurational mean-field ansatz, we obtain the semiclassical backbone of the quantum spectrum through the extremal points of a series of one-dimensional energy landscapes -- each one exhibiting a bifurcation when the external magnetic field drops below a threshold value. The obtained spectra become exact in the limit of vanishing or very strong external, transverse magnetic fields. Further analysis of the higher-order corrections in $1/\sqrt{2S}$ enables us to analytically study the dispersion relations of spin-wave excitations around the semiclassical energy levels. Within the same model, we are able to investigate quantum bifurcations, which occur in the semiclassical ($S\gg 1$) limit, and quantum phase transitions, which are observed in the thermodynamic ($N\rightarrow\infty$) limit.

Signatures of quantum phase transitions in the dynamic response of fluxonium qubit chains

We evaluate the microwave admittance of a one-dimensional chain of fluxonium qubits coupled by shared inductors. Despite its simplicity, this system exhibits a rich phase diagram. A critical applied magnetic flux separates a homogeneous ground state from a phase with a ground state exhibiting inhomogeneous persistent currents. Depending on the parameters of the array, the phase transition may be a conventional continuous one, or of a commensurate-incommensurate nature. Furthermore, quantum fluctuations affect the transition and possibly lead to the presence of gapless "floating phases". The signatures of the soft modes accompanying the transitions appear as a characteristic frequency dependence of the dissipative part of admittance.

Experimental quantification of entanglement through heat capacity

A new experimental realization of heat capacity as an entanglement witness is reported. Entanglement properties of a low–dimensional quantum spin system are investigated by heat capacity measurements performed down to very low temperatures (400 mK), for various applied magnetic field values. The experimentally extracted results for the value of heat capacity at zero field matches perfectly with the theoretical estimates of entanglement from model Hamiltonians. The studied sample is a spin half antiferromagnetic system that shows a clear signature of quantum phase transition at very low temperatures when the heat capacity is varied as a function of fields at a fixed temperature. The variation of entanglement as a function of field is then explored in the vicinity of the quantum phase transition to capture the sudden loss of entanglement.