Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model

Lang, Johannes; Frank, B.; Halimeh, Jad C.

doi:10.1103/physrevb.97.174401

Cited by 98 publications

(127 citation statements)

References 72 publications

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“…Recently, direct experimental observation of DQPTs has been reported, where a transverse-field Ising model was realized with trapped ions [5,6]. For the better understanding of DQPTs several integrable models have been considered [4,[7][8][9][10][11], where the time evolution can be solved exactly. It has been revealed that, like equilibrium phase transitions, DQPTs also affect other observables.…”

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Dynamical Topological Quantum Phase Transitions in Nonintegrable Models

et al. 2019

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We consider sudden quenches across quantum phase transitions in the S = 1 XXZ model starting from the Haldane phase. We demonstrate that dynamical phase transitions may occur during these quenches that are identified by nonanalyticities in the rate function for the return probability. In addition, we show that the temporal behavior of the string order parameter is intimately related to the subsequent dynamical phase transitions. We furthermore find that the dynamical quantum phase transitions can be accompanied by enhanced two-site entanglement.Introduction.-Nonequilibrium dynamics of manybody quantum systems under unitary time evolution continue to pose a challenging problem. The time evolution of a quantum system after a sudden global quench plays a distinguished role in this field since this process can be routinely carried out in experiments and it is addressable in theoretical calculations [1].The quench process is even more interesting when it drives the system through an equilibrium phase transition. This has opened up a new area of research named dynamical quantum phase transitions (DQPTs) [2][3][4]. Although they are not in one-to-one correspondence with the equilibrium phase transitions, but rather a new form of critical behavior, they often emerge when the quench crosses a phase transition. Recently, direct experimental observation of DQPTs has been reported, where a transverse-field Ising model was realized with trapped ions [5,6]. For the better understanding of DQPTs several integrable models have been considered [4,[7][8][9][10][11], where the time evolution can be solved exactly. It has been revealed that, like equilibrium phase transitions, DQPTs also affect other observables. For example, when the quench starts from a broken-symmetry phase, where the order can be characterized by a local order parameter, the order parameter exhibits a temporal decay with a series of times where it vanishes [4,12]. These times usually coincide with the times where the DQPTs occur. The case is more difficult when one considers a nonintegrable model [13][14][15][16][17][18]. Namely, the obvious choice of an observable (e.g. the equilibrium order parameter) may not follow the dynamics dictated by the DQPTs and the connection between them remains elusive like in the case of a nonintegrable Ising chain [19] or Bose-Hubbard model [20]. Thus, the relation of DQPTs to observables in nonintegrable models deserves further investigation in general.In this work we study quenches starting from the Haldane phase to regimes where the ground state has trivial topology. The Haldane phase is a paradigmatic exam-

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Dynamical Topological Quantum Phase Transitions in Nonintegrable Models

et al. 2019

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“…At finite temperature, generalisations of the zero temperature LE were proposed, based on the mixed-state Uhlmann fidelity [45,47], and the interferometric mixed-state geometric phase [48,49]. For an alternative approach to finite-temperature DPTs, see [50,51]. Fidelity is a measure of state distinguishability, which has been employed numerous times in the study of PTs [42,[52][53][54][55], while the interferometric mixed-state geometric phase was introduced in [56].…”

Section: Introductionmentioning

confidence: 99%

Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics

et al. 2018

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We study finite-temperature Dynamical Quantum Phase Transitions (DQPTs) by means of the fidelity and the interferometric Loschmidt Echo (LE) induced metrics. We analyse the associated dynamical susceptibilities (Riemannian metrics), and derive analytic expressions for the case of two-band Hamiltonians. At zero temperature the two quantities are identical, nevertheless, at finite temperatures they behave very differently. Using the fidelity LE, the zero temperature DQPTs are gradually washed away with temperature, while the interferometric counterpart exhibits finitetemperature Phase Transitions (PTs). We analyse the physical differences between the two finitetemperature LE generalisations, and argue that, while the interferometric one is more sensitive and can therefore provide more information when applied to genuine quantum (microscopic) systems, when analysing many-body macroscopic systems, the fidelity-based counterpart is a more suitable quantity to study. Finally, we apply the previous results to two representative models of topological insulators in 1D and 2D. arXiv:1712.01314v2 [cond-mat.stat-mech]

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“…The resulting equations of motion for the average fieldχ and the correlators F , ρ, D F , and D ρ are given in Eqs. (70), (71), (72), (73), and (78), which are complemented by the initial conditions given in Eqs. (79) and (80).…”

Section: Summary Of the Methodsmentioning

confidence: 99%

Nonequilibrium quantum spin dynamics from two-particle irreducible functional integral techniques in the Schwinger boson representation

Schuckert¹,

Orioli²,

Berges³

2018

Phys. Rev. B

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We present a non-equilibrium quantum field theory approach to the initial-state dynamics of spin models based on two-particle irreducible (2PI) functional integral techniques. It employs a mapping of spins to Schwinger bosons for arbitrary spin interactions and spin lengths. At next-to-leading order (NLO) in an expansion in the number of field components, a wide range of non-perturbative dynamical phenomena are shown to be captured, including relaxation of magnetizations in a 3D longrange interacting system with quenched disorder, different relaxation behaviour on both sides of a quantum phase transition and the crossover from relaxation to arrest of dynamics in a disordered spin chain previously shown to exhibit many-body-localization. Where applicable, we employ alternative state-of-the-art techniques and find rather good agreement with our 2PI NLO results. As our method can handle large system sizes and converges relatively quickly to its thermodynamic limit, it opens the possibility to study those phenomena in higher dimensions in regimes in which no other efficient methods exist. Furthermore, the approach to classical dynamics can be investigated as the spin length is increased. arXiv:1806.02347v2 [cond-mat.quant-gas]

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Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model

Cited by 98 publications

References 72 publications

Dynamical Topological Quantum Phase Transitions in Nonintegrable Models

Dynamical Topological Quantum Phase Transitions in Nonintegrable Models

Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics

Nonequilibrium quantum spin dynamics from two-particle irreducible functional integral techniques in the Schwinger boson representation

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