Dynamical quantum phase transitions (Review Article)

Zvyagin, A. A.

doi:10.1063/1.4969869

Cited by 133 publications

(131 citation statements)

References 192 publications

(124 reference statements)

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“…The observed ∼ 1/ scaling of the variance is likely due to the disorder contributions from individual lattices sites being (almost) independent, analogous to the sum of independent random variables in the central limit theorem. This becomes plausible when assuming that (16) holds approximately for weak disorder, and inserting (16) into (21):…”

Section: B Disordered Kitaev Chainmentioning

confidence: 99%

Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems

Mendl

Budich

2019

Phys. Rev. B

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Dynamical quantum phase transitions (DQPTs) represent a counterpart in non-equilibrium quantum time evolution of thermal phase transitions at equilibrium, where real time becomes analogous to a control parameter such as temperature. In quenched quantum systems, recently the occurrence of DQPTs has been demonstrated, both with theory and experiment, to be intimately connected to changes of topological properties. Here, we contribute to broadening the systematic understanding of this relation between topology and DQPTs to multi-orbital and disordered systems. Specifically, we provide a detailed ergodicity analysis to derive criteria for DQPTs in all spatial dimensions, and construct basic counter-examples to the occurrence of DQPTs in multi-band topological insulator models. As a numerical case study illustrating our results, we report on microscopic simulations of the quench dynamics in the Harper-Hofstadter model. Furthermore, going gradually from multiband to disordered systems, we approach random disorder by increasing the (super) unit cell within which random perturbations are switched on adiabatically. This leads to an intriguing order of limits problem which we address by extensive numerical calculations on quenched one-dimensional topological insulators and superconductors with disorder. arXiv:1909.01402v1 [cond-mat.quant-gas]

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Section: B Disordered Kitaev Chainmentioning

confidence: 99%

Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems

Mendl

Budich

2019

Phys. Rev. B

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“…Floquet DQPTs are therefore more accessible to experiments. Thirdly, precisely under the same condition as in (3), our spin chain model is found to reside in a nontrivial "chiral-symmetric" Floquet topological phase [31], as featured by two winding numbers defined with the oneperiod evolution operator in two chiral-symmetric time frames [7]. These two winding numbers can be used to predict topological edge states under open boundary conditions.…”

mentioning

confidence: 96%

“…If pre-quench and post-quench systems are in topologically distinct phases, DQPTs may also be characterized by dynamical topological invariants [3][4][5]. As a promising approach to classify quantum states of matter in nonequilibrium situations, DQPTs have been theoretically explored in both closed and open quantum systems at different physical dimensions [2,7,8]. Experimentally, DQPTs have been observed in trapped ions [3,10], cold atoms [11,12], superconducting qubits [13], nanomechanical oscillators [14], and photonic quantum walks [15,16].To date, in most studies of DQPTs, a quantum quench acts as a trigger for initiating nonequilibrium dynamics and then exposing the underlying topological features.…”

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confidence: 99%

Floquet dynamical quantum phase transitions

et al. 2019

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Dynamical quantum phase transitions (DQPTs) are manifested by time-domain nonanalytic behaviors of many-body systems. Introducing a quench is so far understood as a typical scenario to induce DQPTs. In this work, we discover a novel type of DQPTs, termed "Floquet DQPTs", as intrinsic features of systems with periodic time modulation. Floquet DQPTs occur within each period of continuous driving, without the need for any quenches. In particular, in a harmonically driven spin chain model, we find analytically the existence of Floquet DQPTs in and only in a parameter regime hosting a certain nontrivial Floquet topological phase. The Floquet DQPTs are further characterized by a dynamical topological invariant defined as the winding number of the Pancharatnam geometric phase versus quasimomentum. These findings are experimentally demonstrated with a single spin in diamond. This work thus opens a door for future studies of DQPTs in connection with topological matter.DQPTs are often associated with quantum quenches, a protocol in which parameters of a Hamiltonian are suddenly changed [1,2]. A quantum quench across an equilibrium quantum critical point may induce a DQPT. If pre-quench and post-quench systems are in topologically distinct phases, DQPTs may also be characterized by dynamical topological invariants [3][4][5]. As a promising approach to classify quantum states of matter in nonequilibrium situations, DQPTs have been theoretically explored in both closed and open quantum systems at different physical dimensions [2,7,8]. Experimentally, DQPTs have been observed in trapped ions [3,10], cold atoms [11,12], superconducting qubits [13], nanomechanical oscillators [14], and photonic quantum walks [15,16].To date, in most studies of DQPTs, a quantum quench acts as a trigger for initiating nonequilibrium dynamics and then exposing the underlying topological features. However, DQPTs under more general nonequilibrium manipulations are still largely unexplored [17][18][19]. In particular, because the dynamics of systems under time-periodic modulations has led to fascinating discoveries like Floquet topological states [20-24] and discrete time crystals [25][26][27], it is urgent to investigate how DQPTs may occur in such Floquet systems. Along this avenue, there have been scattered studies, but still with the notion that DQPTs are best aroused by a quench to some system parameters [28,29]. Here we introduce a novel class of DQPTs, termed Floquet DQPTs, which can be regarded as intrinsic features of systems with time-periodic modulations. As schematically shown in Floquet DQPT Time Time Rate function Rate function H i H f (a) H(t) (b) Conventional DQPT T T Quench T FIG. 1. Comparison between (a) DQPTs following a quantum quench, and (b) Floquet DQPTs without any quenches.Here Hi and H f denote the Hamiltonians before and after the quench, H(t) denotes a periodically and continuously modulated Hamiltonian. Fig. 1, the Floquet DQPTs we discovered occur within each period of a continuous driving field, without the need for any...

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“…Often, λ(t) and f (t) show phase-transition like nonanalyticities at time t = t c . These phase transitions in time are the DQPTs [8,10]. TFIM in zero field [14] is defined on a lattice aswhere σ z j is the z-component 2 × 2 Pauli matrix at lattice site j with nearest neighbour interactions favouring an aligned state in the z-direction [15].…”

mentioning

confidence: 99%

“…The signature of DQPT is the nonanalytic behaviour of various quantities in time around critical times t c 's. These transitions have now been shown in many models, like the transverse-field Ising model (TFIM), spin chains, quantum Potts models, the Kitaev model, and many others [1,2,[6][7][8][9][10], and also observed experimentally [11,12]. In spite of being a zerotemperature quantum phenomenon, DQPT is not determined by the quantum phase transitions of the system but rather seems related to the classical thermal criticalities of an associated system [10].…”

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confidence: 99%

Boundaries and Unphysical Fixed Points in Dynamical Quantum Phase Transitions

Khatun

Bhattacharjee

2019

Phys. Rev. Lett.

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We show that dynamic quantum phase transitions (DQPT) in many situations involve renormalization group (RG) fixed points which are unphysical in the context of thermal phase transitions. In such cases, boundary conditions are shown to become relevant to the extent of even completely suppressing the bulk transitions. We establish these by performing exact RG analysis of the quantum Ising model on scale-invariant lattices of different dimensions, and by analyzing the zeros of the Loschmidt amplitude. Further corroboration of boundaries affecting the bulk transition comes from the three-state quantum Potts chain, for which we also show that the DQPT corresponds to a pair of period-2 fixed points.Dynamical quantum phase transitions (DQPT), a recent discovery of phase transitions, often periodic, in large quantum systems during time evolution [1-3], have generated a lot of interest because here time itself acts as the parameter inducing the transitions. Also, to be at a transition point, only time needs to be chosen properly without any requirement of fine-tuning of system parameters, unlike thermal transitions [4]. The signature of DQPT is the nonanalytic behaviour of various quantities in time around critical times t c 's. These transitions have now been shown in many models, like the transverse-field Ising model (TFIM), spin chains, quantum Potts models, the Kitaev model, and many others[1, 2, 6-10], and also observed experimentally [11,12]. In spite of being a zerotemperature quantum phenomenon, DQPT is not determined by the quantum phase transitions of the system but rather seems related to the classical thermal criticalities of an associated system [10]. However, despite the use of many techniques so far, very few exact results are known on the scaling and universality in DQPT [10]. Moreover, the natures of the possible phases and the transitions remain to be properly classified, e. g., whether only equilibrium phases and transitions would suffice or there can be specialities of its own [10].A general approach for phase transitions is the renormalization group (RG) framework [5] in terms of lengthdependent effective parameters and their flows to the fixed points (FP), with the stable FPs determining the allowed phases, and the unstable ones (or separatrices) the phase transitions. In this paper, we adopt an exact RG scheme for TFIM and the three-state quantum Potts chain (3QPC). Our exact results establish that there are DQPTs involving FPs that are unphysical in traditional thermal transitions. Secondly, we show that, for those unphysical FPs, boundary conditions (BC) are relevant and can even lead to a suppression of the transitions completely, unlike thermal cases where BCs do not affect the bulk transitions. Another surprising result is the emergence of a pair of period-2 FPs, never seen in the thermal context, that controls the DQPT in 3QPC, in contrast to the zero-temperature FP [2] for the Ising DQPT case. In short, our exact results bring out several distinctive features of DQPT, not to be found in equil...

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Dynamical quantum phase transitions (Review Article)

Cited by 133 publications

References 192 publications

Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems

Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems

Floquet dynamical quantum phase transitions

Boundaries and Unphysical Fixed Points in Dynamical Quantum Phase Transitions

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