arXiv subjects

Bo-Bo Wei

Publications and source records attributed to Bo-Bo Wei.

At least 19 recordsLinked to original sources

arXiv2020

Dynamical quantum phase transitions in a spin chain with deconfined quantum critical points

We analytically and numerically study the Loschmidt echo and the dynamical order parameters in a spin chain with a deconfined phase transition between a dimerized state and a ferromagnetic phase. For quenches from a dimerized state to a ferromagnetic phase, we find that the model can exhibit a dynamical quantum phase transition characterized by an associating dimerized order parameters. In particular, when quenching the system from the Majumdar-Ghosh state to the ferromagnetic Ising state, we find an exact mapping into the classical Ising chain for a quench from the paramagnetic phase to the classical Ising phase by analytically calculating the Loschmidt echo and the dynamical order parameters. By contrast, for quenches from a ferromagnetic state to a dimerized state, the system relaxes very fast so that the dynamical quantum transition may only exist in a short time scale. We reveal that the dynamical quantum phase transition can occur in systems with two broken symmetry phases and the quench dynamics may be independent on equilibrium phase transitions.

cond-mat.stat-mech↗

arXiv2020

Hybrid exceptional point created from type III Dirac point

Degeneracy (exceptional) points embedded in energy band are distinct by their topological features. We report different hybrid two-state coalescences (EP2s) formed through merging two EP2s with opposite chiralities that created from the type III Dirac points emerging from a flat band. The band touching hybrid EP2, which is isolated, is induced by the destructive interference at the proper match between non-Hermiticity and synthetic magnetic flux. The degeneracy points and different types of exceptional points are distinguishable by their topological features of global geometric phase associated with the scaling exponent of phase rigidity. Our findings not only pave the way of merging EPs but also shed light on the future investigations of non-Hermitian topological phases.

cond-mat.mes-hall↗

arXiv2019

Experimental Observation of Equilibrium and Dynamical Quantum Phase Transitions via Out-of-Time-Ordered Correlators

The out-of-time-ordered correlators (OTOC) have been established as a fundamental concept for quantifying quantum information scrambling and diagnosing quantum chaotic behavior. Recently, it was theoretically proposed that the OTOC can be used as an order parameter to dynamically detect both equilibrium quantum phase transitions (EQPTs) and dynamical quantum phase transitions (DQPTs) in one-dimensional many-body systems. Here we report the first experimental observation of EQPTs and DQPTs in a quantum spin chain via quench dynamics of OTOC on a nuclear magnetic resonance quantum simulator. We observe that the quench dynamics of both the order parameter and the two-body correlation function cannot detect the DQPTs, but the OTOC can unambiguously detect the DQPTs. Moreover, we demonstrate that the long-time average value of the OTOC in quantum quench signals the equilibrium quantum critical point and ordered quantum phases, thus one can measure the EQPTs from the non-equilibrium quantum quench dynamics. Our experiment paves a way for experimentally investigating DQPTs through OTOCs and for studying the EQPTs through the non-equilibrium quantum quench dynamics with quantum simulators.

quant-ph↗

arXiv2019

Fidelity as a probe for a deconfined quantum critical point

Deconfined quantum critical point was proposed as a second-order quantum phase transition between two broken symmetry phases beyond the Landau-Ginzburg-Wilson paradigm. However, numerical studies cannot completely rule out a weakly first-order transition because of strong violations of finite-size scaling. We demonstrate that the fidelity is a simple probe to study deconfined quantum critical point. We study the ground-state fidelity susceptibility close to the deconfined quantum critical point in a spin chain using the large-scale finite-size density matrix renormalization group method. We find that the finite-size scaling of the fidelity susceptibility obeys the conventional scaling behavior for continuous phase transitions, supporting the deconfined quantum phase transition is continuous. We numerically determine the deconfined quantum critical point and the associated correlation length critical exponent from the finite-size scaling theory of the fidelity susceptibility. Our results are consistent with recent results obtained directly from the matrix product states for infinite-size lattices using others observables. Our work provides a useful probe to study critical behaviors at deconfined quantum critical point from the concept of quantum information.

cond-mat.str-el↗

arXiv2019

Dynamical Scaling Laws of Out-of-Time-Ordered Correlators

The out-of-time-ordered correlator (OTOC) is central to the understanding of information scrambling in quantum many-body systems. In this work, we show that the OTOC in a quantum many-body system close to its critical point obeys dynamical scaling laws which are specified by a few universal critical exponents of the quantum critical point. Such scaling laws of the OTOC imply a universal form for the butterfly velocity of a chaotic system in the quantum critical region and allow one to locate the quantum critical point and extract all universal critical exponents of the quantum phase transitions. We numerically confirm the universality of the butterfly velocity in a chaotic model, namely the transverse axial next-nearest-neighbor Ising model, and show the feasibility of extracting the critical properties of quantum phase transitions from OTOC using the Lipkin-Meshkov-Glick (LMG) model.

quant-ph↗

arXiv2019

Universality in the Decay and Revival of Loschmidt Echoes

A critically enhanced decay of the Loschmidt echo is characteristic of sudden quench dynamics near a quantum phase transition. Here, we demonstrate that the decay and revival of the Loschmidt echo follows power-law scaling in the system size and the distance from a critical point with equilibrium critical exponents. We reveal such dynamical scaling laws by analyzing relevant perturbations to the Loschmidt echo cast in a scaling invariant form. We confirm the validity and the generality of the predicted dynamical scaling laws with a diverse range of critical models such as Ising spin models with a short and long range interaction, a finite-component system phase transition, and a topological phase transition. Moreover, using the integrability of systems in the thermodynamic limit, we derive such scaling laws analytically from a microscopic analysis. Our finding promotes the Loschmidt echo to a quantitative non-equilibrium probe of criticality and allows for quantitative predictions on the role of criticality on various physical scenarios where the Loschmidt echo is central to describing non-equilibrium dynamics.

quant-ph↗

arXiv2019

Fidelity Susceptibility in One-dimensional Disordered Lattice Models

We investigate quantum phase transitions in one-dimensional quantum disordered lattice models, the Anderson model and the Aubry-André model, from the fidelity susceptibility approach. First, we find that the fidelity susceptibility and the generalized adiabatic susceptibility are maximum at the quantum critical points of the disordered models, through which one can locate the quantum critical point in disordered lattice models. Second, finite-size scaling analysis of the fidelity susceptibility and of the generalized adiabatic susceptibility show that the correlation length critical exponent and the dynamical critical exponent at the quantum critical point of the one-dimensional Anderson model are respectively 2/3 and 2 and of the Aubry-André model are respectively 1 and 2.375. Thus the quantum phase transitions in the Anderson model and in the Aubry-André model are of different universality classes. Because the fidelity susceptibility and the generalized adiabatic susceptibility are directly connected to the dynamical structure factor which are experimentally accessible in the linear response regime, the fidelity susceptibility in quantum disordered systems may be observed experimentally in near future.

cond-mat.stat-mech↗

arXiv2018

Probing Conformal Invariant of Non-unitary Two-Dimensional Systems by Central Spin Decoherence

Universality classes of non-unitary critical theories in two-dimensions are characterized by a dimensional number, termed central charge or conformal anomaly. Conformal invariance predicts that the leading finite-size correction to the free energy of a two-dimensional system at a conformal invariant critical point is linearly related to the central charge of the corresponding conformal field theory. However, experimental determination of the central charge of a non-unitary conformal invariant critical theory has not been done before because of the intrinsic difficulty that complex parameters occurs in non-unitary theory, which is not physical. Here we propose to extract the central charge of the non-unitary conformal invariant critical point of a two-dimensional lattice models from the quantum coherence measurement of a probe spin which is coupled to the two-dimensional lattice models. A recent discovery shows that quantum decoherence of a probe spin which is coupled to a bath is proportional to the partition function of the bath with a complex parameter. Thus the central charge of a non-unitary conformal field theory could be extracted from quantum decoherence measurement of a probe spin which is coupled to a bath. We have applied the method to a typical non-unitary conformal invariant critical theory, namely the Yang-Lee edge singularity of the two-dimensional Ising model and extracted the central charge of the Yang-Lee edge singularity in two-dimensional Ising model with good precision and tested other predictions of non-unitary conformal field theory. This work paves the way for the first experimental observation of the central charge of non-unitary conformal field theory.

cond-mat.stat-mech↗

arXiv2018

Linking Phase Transitions and Quantum Entanglement at Arbitrary Temperature

In this work, we establish a general theory of phase transitions and quantum entanglement in the equilibrium state at arbitrary temperatures. First, we derived a set of universal functional relations between the matrix elements of two-body reduced density matrix of the canonical density matrix and the Helmholtz free energy of the equilibrium state, which implies that the Helmholtz free energy and its derivatives are directly related to entanglement measures because any entanglement measures are defined as a function of the reduced density matrix. Then we show that the first order phase transitions are signaled by the matrix elements of reduced density matrix while the second order phase transitions are witnessed by the first derivatives of the reduced density matrix elements. Near second order phase transition point, we show that the first derivative of the reduced density matrix elements present universal scaling behaviors. Finally we establish a theorem which connects the phase transitions and entanglement at arbitrary temperatures. Our general results are demonstrated in an experimentally relevant many-body spin model.

quant-ph↗

arXiv2017

Fluctuation Relations for Heat Exchange in the Generalized Gibbs Ensemble

In this work, we investigate the heat exchange between two quantum systems whose initial equilibrium states are described by the generalized Gibbs ensemble. First, we generalize the fluctuation relations for heat exchange discovered by Jarzynski and Wójcik to quantum systems prepared in the equilibrium states described by the generalized Gibbs ensemble at different generalized temperatures. Second, we extend the connections between heat exchange and Rényi divergences to quantum systems with very general initial conditions.These relations are applicable for quantum systems with conserved quantities and are universally valid for quantum systems in the integrable and chaotic regimes.

quant-ph↗

arXiv2017

Relations between Heat Exchange and Rényi Divergences

In this work, we establish an exact relation which connects the heat exchange between two systems initialized in their thermodynamic equilibrium states at different temperatures and the Rényi divergences between the initial thermodynamic equilibrium state and the final non-equilibrium state of the total system. The relation tells us that the various moments of the heat statistics are determined by the Renyi divergences between the initial equilibrium state and the final non-equilibrium state of the global system. In particular the average heat exchange is quantified by the relative entropy between the initial equilibrium state and the final non-equilibrium state of the global system. The relation is applicable to both finite classical systems and finite quantum systems.

quant-ph↗

arXiv2017

Dissipation in the Generalized Gibbs Ensemble

In this work, we show that the dissipation in a many-body system under an arbitrary non-equilibrium process is related to the Rényi divergences between two states along the forward and reversed dynamics under very general family of initial conditions. This relation generalizes the links between dissipated work and Renyi divergences to quantum systems with conserved quantities whose equilibrium state is described by the generalized Gibbs ensemble. The relation is applicable for quantum systems with conserved quantities and can be applied to protocols driving the system between integrable and chaotic regimes. We demonstrate our ideas by considering the one-dimensional transverse quantum Ising model which is driven out of equilibrium by the instantaneous switching of the transverse magnetic field.

cond-mat.stat-mech↗

arXiv2017

Quantum Work Relations and Response Theory in $\mathcal{PT}$-Symmetric Quantum Systems

In this work, we show that a universal quantum work relation for a quantum system driven arbitrarily far from equilibrium extend to $\mathcal{PT}$-symmetric quantum system with unbroken $\mathcal{PT}$ symmetry, which is a consequence of microscopic reversibility. The quantum Jarzynski equality, linear response theory and Onsager reciprocal relations for the $\mathcal{PT}$-symmetric quantum system are recovered as special cases of the universal quantum work relation in $\mathcal{PT}$-symmetric quantum system. In the regime of broken $\mathcal{PT}$ symmetry, the universal quantum work relation does not hold as the norm is not preserved during the dynamics.

cond-mat.stat-mech↗

arXiv2017

Links between Dissipation and Rényi Divergences in $\mathcal{PT}$-Symmetric Quantum Mechanics

Thermodynamics and information theory have been intimately related since the times of Maxwell and Boltzmann. Recently it was shown that the dissipated work in an arbitrary non-equilibrium process is related to the Rényi divergences between two states along the forward and reversed dynamics. Here we show that the relation between dissipated work and Renyi divergences generalizes to $\mathcal{PT}$-symmetric quantum mechanics with unbroken $\mathcal{PT}$ symmetry. In the regime of broken $\mathcal{PT}$ symmetry, the relation between dissipated work and Renyi divergences does not hold as the norm is not preserved during the dynamics. This finding is illustrated for an experimentally relevant system of two-coupled cavities.

cond-mat.stat-mech↗

arXiv2017

Fidelity Susceptibility in the Quantum Rabi Model

Quantum criticality usually occurs in many-body systems. Recently it was shown that the quantum Rabi model, which describes a two-level atom coupled to a single model cavity field, presents quantum phase transitions from a normal phase to a superradiate phase when the ratio between the frequency of the two level atom and the frequency of the cavity field extends to infinity. In this work, we study quantum phase transitions in the quantum Rabi model from the fidelity susceptibility perspective. We found that the fidelity susceptibility and the generalized adiabatic susceptibility present universal finite size scaling behaviors near the quantum critical point of the Rabi model if the ratio between frequency of the two level atom and frequency of the cavity field is finite. From the finite size scaling analysis of the fidelity susceptibility, we found that the adiabatic dimension of the fidelity susceptibility and the generalized adiabatic susceptibility of fourth order in the Rabi model are $4/3$ and $2$, respectively. Meanwhile the correlation length critical exponent and the dynamical critical exponent in the quantum critical point of the Rabi model are found to be $3/2$ and $1/3$ respectively. Since the fidelity susceptibility and the generalized adiabatic susceptibility are the moments of the quantum noise spectrum which is directly measurable by experiments in linear response regime, the scaling behavior of the fidelity susceptibility in the Rabi model could be tested experimentally. The simple structure of the quantum Rabi model paves the way for experimentally observing the universal scaling behavior of the fidelity susceptibility at a quantum phase transition.

quant-ph↗

arXiv2017

Extracting the Central Charge of Conformal Field Theory by Central Spin Decoherence

Conformal invariance powerfully constrains the critical behavior of two-dimensional classical systems with short-range interactions and the critical theories in two-dimensions are parametrized by a dimensional number, termed central charge or conformal anomaly $c$. However, experimental determination of the central charge of a conformal field theory has not been done before. Here we propose to extract the central charge of the conformal field theory corresponding to a critical point of a two-dimensional lattice models from the quantum decoherence measurement of a probe spin which is coupled to the two-dimensional lattice models. Conformal invariance predicts that the leading finite-size correction to the free energy for a two-dimensional system at a conformal invariant critical point is linearly related to the conformal anomaly for various boundary conditions. A recent discovery of thermodynamic holography allows us to obtain the free energy of many-body system from central spin decoherence measurement. Thus the central charge of the conformal field theory could be extracted from central spin decoherence measurement. We have applied the method to the two-dimensional Ising model and extracted the central charge of two-dimensional Ising model with good precision. This work provides a useful approach to extracting the central charge of conformal field theory in various two-dimensional lattice systems.

quant-ph↗

arXiv2016

Probing Yang-Lee Edge Singularity by Central Spin Decoherence

Yang-Lee edge singularities are the branch point of the free energy on the complex plane of physical parameters and were shown to be the simplest universality class of phase transitions. However, the Yang-Lee edge singularities have not been regarded as experimentally observable since they occur at complex physical parameters, which are unphysical. A recent discovery about the relation between partition functions and probe spin coherence makes it experimentally feasible to access the complex plane of physical parameters. However, how to extract the critical point and the critical exponent of Yang-Lee edge singularities in many-body systems, which occurs only at thermodynamic limit, has still been elusive. Here we show that the quantum coherence of a probe spin coupled to finite-size Ising-type spin systems presents universal scaling behavior near the Yang-Lee edge singularity. The finite-size scaling behavior of quantum coherence of the probe spin predicts that one can extract the critical point and the critical exponent of the Yang-Lee edge singularity of Ising-type spin system in the thermodynamic limit from the spin coherence measurement of the probe spin coupled to finite Ising-type spin systems. This finding provides a practical approach to studying the nature of Yang-Lee edge singularities of many-body systems.

cond-mat.stat-mech↗

arXiv2016

Universal Critical Behaviors in Non-Hermitian Phase Transitions

Quantum phase transitions also occur in non-Hermitian systems. In this work we show that density functional theory, for the first time, uncovers universal behaviors for phase transitions in non-Hermitian many-body systems. To be specific, we first prove that the non-degenerate steady state of a non-Hermitian quantum many-body system is a universal function of the first derivative of the steady state energy with respect to the control parameter. This finding has far-reaching consequences for non-Hermitian systems: (i) It bridges the nonanalytic behavior in physical observable and nonanalytic behavior of steady state energy, which explains why the quantum phase transitions in non-Hermitian systems occur for finite systems. (ii) It predicts universal scaling behaviors of any physical observable at non-Hermitian phase transition point with scaling exponent being $(1-1/p),2(1-1/p),\cdots,n(1-1/p),\cdots$ with $p$ being the number of coalesced states at the exceptional point and $n$ being a positive integer. (iii). It reveals that quantum entanglement in non-Hermitian phase transition point presents universal scaling behaviors with critical exponents being $(1-1/p),2(1-1/p),\cdots,n(1-1/p),\cdots$. These results uncover universal critical behaviors in non-Hermitian phase transitions and provide profound connections between entanglement and phase transition in non-Hermitian quantum many-body physics and establish foundations for quantum metrology in non-Hermitian systems.

quant-ph↗