Detection of Quantum Phases via Out-of-Time-Order Correlators

Dağ, Ceren B.; Sun, Kai; Duan, L.-M.

doi:10.1103/physrevlett.123.140602

Cited by 60 publications

(32 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast, under periodic boundary conditions (yellow diamonds line) and for a bulk spin W = V = σ z bulk (green left-pointing triangles), the OTOC no longer differentiates the two phases, and the transition point is smoothed out consistent with predictions from Ref. 20 .…”

Section: Demonstration Of Topological Originsupporting

confidence: 77%

“…Out-of-time-order correlators (OTOCs) have become a widely-appreciated tool to measure the correlation buildup in space and time, and hence quantitatively characterize information scrambling in interacting many-body systems [1][2][3][4][5] . Started off as a theoretical tool to understand quantum information in a black hole 6,7 its impact quickly expanded to a wide variety of subjects including but not limited to: quantum chaos [8][9][10][11][12] , many-body localization 3,10,[13][14][15] , quantum integrability 9,12,16,17 , quantum criticality 18 and recently symmetry-breaking quantum phase transitions 19,20 .…”

Section: Introductionmentioning

confidence: 99%

“…In this manuscript, we focus on the regime starting shortly after the (initial) decay of OTOC and lasts for a time interval of T . It has been recently found that the OTOC saturation value at zero-temperature exhibits order parameter-like behavior, and thus can directly probe the long-range quantum order and quan-tum phase transitions 20 . In contrast to the naive intuition, where thermal fluctuations wash away low energy quantum effects at high temperature, in this work we observe an emergent relation between infinite-temperature information scrambling and zero-temperature Z 2 topological order in the bulk in multiple model systems, e.g.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Topologically induced prescrambling and dynamical detection of topological phase transitions at infinite temperature

2020

Self Cite

View full text Add to dashboard Cite

We report a numerical observation where the infinite-temperature out-of-time-order correlators (OTOCs) directly probe quantum phase transitions at zero temperature, in contrast to common intuition where low energy quantum effects are washed away by strong thermal fluctuations at high temperature. By comparing numerical simulations with exact analytic results, we determine that this phenomenon has a topological origin and is highly generic, as long as the underlying system can be mapped to a 1D Majorana chain. Using the Majorana basis, we show that the infinite-temperature OTOCs probe zero-temperature quantum phases via detecting the presence of Majorana zero modes at the ends of the chain that is associated with 1D Z2 topological order. Hence, we show that strong zero modes also affect OTOCs and scrambling dynamics. Our results demonstrate an intriguing interplay between information scrambling and topological order, which leads to a new phenomenon in the scrambling of generic non-integrable models: topological order induced pre-scrambling, paralleling the notion of prethermalization of two-time correlators, that defines a time-scale for the restricted scrambling of topologically-protected quantum information.

show abstract

Section: Demonstration Of Topological Originsupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Topologically induced prescrambling and dynamical detection of topological phase transitions at infinite temperature

2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…Various kinds of OTOCs in quantum maps were also studied[20][21][22][23]. The cases with large N are found in[24][25][26][27][28][29][30][31][32][33][34][35].…”

mentioning

confidence: 99%

Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator

Hashimoto

Huh

Kim

et al. 2020

J. High Energ. Phys.

View full text Add to dashboard Cite

We provide a detailed examination of a thermal out-of-time-order correlator (OTOC) growing exponentially in time in systems without chaos. The system is a one-dimensional quantum mechanics with a potential whose part is an inverted harmonic oscillator. We numerically observe the exponential growth of the OTOC when the temperature is higher than a certain threshold. The Lyapunov exponent is found to be of the order of the classical Lyapunov exponent generated at the hilltop, and it remains non-vanishing even at high temperature. We adopt various shape of the potential and find these features universal. The study confirms that the exponential growth of the thermal OTOC does not necessarily mean chaos when the potential includes a local maximum. We also provide a bound for the Lyapunov exponent of the thermal OTOC in generic quantum mechanics in one dimension, which is of the same form as the chaos bound obtained by Maldacena, Shenker and Stanford.

show abstract

“…Nevertheless, the quenched dynamics of Rényi entropy in cavity–atom interaction systems and its linkage between the QPTs and chaos in the systems are worthwhile to study further. On the other hand, this work could also enlighten the investigations of thermal‐averaged OTOCs in condensed‐matter systems71–73 and other quantum optics systems such as driven Tavis–Cummings model 67. With the rapid development of quantum simulation46,48–54,74–76 and general measurement protocol of OTOCs,77 we believe that our results may provide an experimentally feasible approach to detect equilibrium quantum critical points and find the universal properties of few‐body systems in quantum region.…”

Section: Discussionmentioning

confidence: 70%

Out‐of‐Time‐Order Correlators and Quantum Phase Transitions in the Rabi and Dicke Models

et al. 2020

View full text Add to dashboard Cite

The out-of-time-order correlators (OTOCs) is used to study the quantum phase transitions (QPTs) between the normal phase and the superradiant phase in the Rabi and few-body Dicke models with large frequency ratio of the atomic level splitting to the single-mode electromagnetic radiation field frequency. The focus is on the OTOC thermally averaged with infinite temperature, which is an experimentally feasible quantity. It is shown that the critical points can be identified by long-time averaging of the OTOC via observing its local minimum behavior. More importantly, the scaling laws of the OTOC for QPTs are revealed by studying the experimentally accessible conditions with finite frequency ratio and finite number of atoms in the studied models. The critical exponents extracted from the scaling laws of OTOC indicate that the QPTs in the Rabi and Dicke models belong to the same universality class.

show abstract

Detection of Quantum Phases via Out-of-Time-Order Correlators

Cited by 60 publications

References 34 publications

Topologically induced prescrambling and dynamical detection of topological phase transitions at infinite temperature

Topologically induced prescrambling and dynamical detection of topological phase transitions at infinite temperature

Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator

Out‐of‐Time‐Order Correlators and Quantum Phase Transitions in the Rabi and Dicke Models

Contact Info

Product

Resources

About