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

Mera, Bruno; Vlachou, Chrysoula; Paunković, Nikola; Vieira, V. R.; Viyuela, Oscar

doi:10.1103/physrevb.97.094110

Cited by 71 publications

(49 citation statements)

References 73 publications

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“…Therefore the LO defined in the fidelity approach in Eq. (3) will not be able to capture DQPTs during the dissipative evolution as also observed in [64].…”

Section: A Fidelity Induced Loschmidt Overlapmentioning

confidence: 99%

Exploring the possibilities of dynamical quantum phase transitions in the presence of a Markovian bath

Bandyopadhyay¹,

Sudarshana²,

Bhattacharya³

et al. 2018

Sci Rep

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We explore the possibility of dynamical quantum phase transitions (DQPTs) occurring during the temporal evolution of a quenched transverse field Ising chain coupled to a particle loss type of bath (local in Jordan-Wigner fermion space) using two versions of the Loschmidt overlap (LO), namely, the fidelity induced LO and the interferometric phase induced LO. The bath, on the one hand, dictates the dissipative evolution following a sudden quench and on the other, plays a role in dissipative mixed state preparation in the later part of the study. During a dissipative evolution following a sudden quench, no trace of DQPTs are revealed in both the fidelity and the interferometric phase approaches; however, remarkably the interferometric phase approach reveals the possibility of inter-steady state DQPTs in passage from one steady state to the other when the system is subjected to a quench after having reached the first steady state. We further probe the occurrences of DQPTs when the system evolves unitarily after being prepared in a mixed state of engineered purity by ramping the transverse field in a linear fashion in the presence of the bath. In this case though the fidelity approach fails to indicate any DQPT, the interferometric approach indeed unravels the possibility of occurrence of DQPTs which persists even up to a considerable loss of purity of the engineered initial state as long as a constraint relation involving the dissipative coupling and ramping time (rate) is satisfied. This constraint relation also marks the boundary between two dynamically inequivalent phases; in one the LO vanishes for the critical momentum mode (and hence DQPTs exist) while in the other no such critical mode can exist and hence the LO never vanishes.

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“…Therefore the LO defined in the fidelity approach in Eq. (3) will not be able to capture DQPTs during the dissipative evolution as also observed in [64].…”

Section: A Fidelity Induced Loschmidt Overlapmentioning

confidence: 99%

Exploring the possibilities of dynamical quantum phase transitions in the presence of a Markovian bath

Bandyopadhyay¹,

Sudarshana²,

Bhattacharya³

et al. 2018

Sci Rep

View full text Add to dashboard Cite

show abstract

“…It is therefore interesting to generalise the concept of dynamical phase transitions to finite temperatures and density matrices. 29,[35][36][37][38][39] There is no unique way in which one may want to make such a figure 5(a). The solid dashed line is the entanglement entropy for cutting two dimers.…”

Section: Finite Temperaturesmentioning

confidence: 99%

Dynamical Phase Transitions in Topological Insulators

Sedlmayr

2019

Acta Phys. Pol. A

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The traditional concept of phase transitions has, in recent years, been widened in a number of interesting ways. The concept of a topological phase transition separating phases with a different ground state topology, rather than phases of different symmetries, has become a large widely studied field in its own right. Additionally an analogy between phase transitions, described by nonanalyticities in the derivatives of the free energy, and non-analyticities which occur in dynamically evolving correlation functions has been drawn. These are called dynamical phase transitions and one is often now far from the equilibrium situation. In these short lecture notes we will give a brief overview of the history of these concepts, focusing in particular on the way in which dynamical phase transitions themselves can be used to shed light on topological phase transitions and topological phases. We will go on to focus, first, on the effect which the topologically protected edge states, which are one of the interesting consequences of topological phases, have on dynamical phase transitions. Second we will consider what happens in the experimentally relevant situations where the system begins either in a thermal state rather than the ground state, or exchanges particles with an external environment. arXiv:1910.02314v2 [cond-mat.mes-hall]

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“…Moreover, DQPTs appear to be robust against small symmetrypreserving perturbations, meaning that their presence cannot make DQPTs disappear but they only contribute with some minor effects such as a shift in the critical time [9][10][11] . Also dynamical order parameters have been identified 6,[12][13][14]19,20 which have been successful in characterizing DQPTs occurring in topological systems [21][22][23][24][25] .…”

Section: Dynamical Quantum Phase Transitionsmentioning

confidence: 99%

Constructing effective free energies for dynamical quantum phase transitions in the transverse-field Ising chain

Trapin

Heyl

2018

Phys. Rev. B

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The theory of dynamical quantum phase transitions represents an attempt to extend the concept of phase transitions to the far from equilibrium regime. While there are many formal analogies to conventional transitions, it is a major question to which extent it is possible to formulate a nonequilibrium counterpart to a Landau-Ginzburg theory. In this work we take a first step in this direction by constructing an effective free energy for continuous dynamical quantum phase transitions appearing after quantum quenches in the transverse-field Ising chain. Due to unitarity of quantum time evolution this effective free energy becomes a complex quantity transforming the conventional minimization principle of the free energy into a saddle-point equation in the complex plane of the order parameter, which as in equilibrium is the magnetization. We study this effective free energy in the vicinity of the dynamical quantum phase transition by performing an expansion in terms of the complex magnetization and discuss the connections to the equilibrium case. Furthermore, we study the influence of perturbations and signatures of these dynamical quantum phase transitions in spin correlation functions. arXiv:1802.00020v3 [cond-mat.stat-mech]

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

Cited by 71 publications

References 73 publications

Exploring the possibilities of dynamical quantum phase transitions in the presence of a Markovian bath

Exploring the possibilities of dynamical quantum phase transitions in the presence of a Markovian bath

Dynamical Phase Transitions in Topological Insulators

Constructing effective free energies for dynamical quantum phase transitions in the transverse-field Ising chain

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