Mixed state dynamical quantum phase transitions

Bhattacharya, Utso; Bandyopadhyay, Souvik; Dutta, Amit

doi:10.1103/physrevb.96.180303

Cited by 112 publications

(107 citation statements)

References 104 publications

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“…Further studies, however, revealed that DQPTs can occur following a quench also within the same phase [48][49][50]. Other theoretical works have explored DQPTs in topological and mixed phases [72][73][74][75][76] and also after slow quenches ("ramps") [77][78][79].…”

Section: Dynamical Quantum Phase Transitionsmentioning

confidence: 99%

Quench dynamics and zero-energy modes: The case of the Creutz model

et al. 2019

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In most lattice models, the closing of a band gap typically occurs at high-symmetry points in the Brillouin zone. Differently, in the Creutz model − describing a system of spinless fermions hopping on a two-leg ladder pierced by a magnetic field − the gap closing at the quantum phase transition between the two topologically nontrivial phases of the model can be moved by tuning the hopping amplitudes. We take advantage of this property to examine the nonequilibrium dynamics of the model after a sudden quench of the magnetic flux through the plaquettes of the ladder. For a quench to one of the equilibrium quantum critical points we find that the revival period of the Loschmidt echo − measuring the overlap between initial and time-evolved states − is controlled by the gap closing zero-energy modes. In particular, and contrary to expectations, the revival period of the Loschmidt echo for a finite ladder does not scale linearly with size but exhibits jumps determined by the presence or absence of zero-energy modes. We further investigate the conditions for the appearance of dynamical quantum phase transitions in the model and find that, for a quench to an equilibrium critical point, such transitions occur only for ladders of sizes which host zero-energy modes. Exploiting concepts from quantum thermodynamics, we show that the average work and the irreversible work per lattice site exhibit a weak dependence on the size of the system after a quench across an equilibrium critical point, suggesting that quenching into a different phase induces effective correlations among the particles.

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Section: Dynamical Quantum Phase Transitionsmentioning

confidence: 99%

Quench dynamics and zero-energy modes: The case of the Creutz model

et al. 2019

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“…At the end of this section, we give a short remark on the comparison of our GLOA and GLOA in Refs. [39,40]. All GLOAs take a very similar form but show a considerable difference for the unitary evolution for mixed states.…”

Section: Finite Temperature Effectmentioning

confidence: 93%

“…The generalizations of LOA are not unique. The previous results focus on the different aspects and give the different generalizations, which are applicable in some situations [37][38][39][40][41][42] . One class of generalizations is based on quasi-distance approaches.…”

Section: Loschmidt Overlap Amplitude and Dynamical Topological Ormentioning

confidence: 99%

Dynamical quantum phase transition for mixed states in open systems

et al. 2018

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Based on a kinematic approach in defining a geometric phase for a density matrix, we define the generalized Loschmidt overlap amplitude (GLOA) for an open system for arbitrary quantum evolution. The GLOA reduces to the Loschmidt overlap amplitude (LOA) with a modified dynamic phase for unitary evolution of a pure state, with the argument of the GLOA well-defined by the geometric phase, thus possessing similar physical interpretation to that of the LOA. The rate function for the GLOA exhibits non-analyticity at a critical time, which corresponds to the dynamical quantum phase transition. We observe that the dynamical quantum phase transition related to GLOA is not destroyed under a finite temperature and weak enough dissipation. In particular, we find that a new type of dynamical quantum phase transition emerges in a dissipation system. The proposed GLOA provides a powerful tool in the investigation of a dynamical quantum phase transition in an arbitrary quantum system, which not only can characterize the robustness of the dynamical quantum phase transition but also can be used to search for new transitions.

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“…Near a characteristic time scale that is inversely proportional to the interaction strength, there exist critical times, t c , characterizing the transitions between different types of Schrödinger's cats. Moreover, different from other DQPTs that have been studied in the literature [18,24,[26][27][28][29][30][31], t c here by itself corresponds to the rise of a pair condensate, a premier example of exotic condensate featured with vanishing one-body correlation function and prevailing two-body correlations [32][33][34]. As for the dynamically generated Schrödinger's cats, they are much more stable than those at equilibrium.…”

mentioning

confidence: 89%

“…With increasing N , discrete zeros merge to continuous manifolds and eventually touch the real t axis, making physical observables nonanalytic, similar to Lee-Yang zeros and Fisher zeros in the complex plane of the temperature or other parameters [22,23]. Whereas observations of DQPTs have been reported in certain spin systems [18,[24][25][26][27][28], such novel concept well deserves both theoretical and experimental studies in a much broader range of systems.…”

mentioning

confidence: 99%

Dynamical quantum phase transitions in interacting atomic interferometers

Lyu

Zhou

2020

Phys. Rev. A

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Particle-wave duality has allowed physicists to establish atomic interferometers as celebrated complements to their optical counterparts in a broad range of quantum devices. However, interactions naturally lead to decoherence and have been considered as a longstanding obstacle in implementing atomic interferometers in precision measurements. Here, we show that interactions lead to dynamical quantum phase transitions between Schrödinger's cats in an atomic interferometer. These transition points result from zeros of Loschmidt echo, which approach the real axis of the complex time plane in the large particle number limit, and signify pair condensates, another type of exotic quantum states featured with prevailing two-body correlations. Our work suggests interacting atomic interferometers as a new tool for exploring dynamical quantum phase transitions and creating highly entangled states to beat the standard quantum limit.

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Mixed state dynamical quantum phase transitions

Cited by 112 publications

References 104 publications

Quench dynamics and zero-energy modes: The case of the Creutz model

Quench dynamics and zero-energy modes: The case of the Creutz model

Dynamical quantum phase transition for mixed states in open systems

Dynamical quantum phase transitions in interacting atomic interferometers

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