DYNAMICAL PHASE TRANSITIONS ON COMB LATTICES

We study by analytical techniques the dynamical phase transition between recursive and transient regime induced on comb lattices by a topological bias. The critical exponents are expressed as functions of the intrinsic dimensions of these structures. In particular we show that, unlike what happens on Bethe lattices, it takes in general two different exponents to characterize the approach to the critical point from the recursive phase and from the transient one. These exponents depend respectively on the connectivity and on the spectral dimension.

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Dynamical Phase Transition of Biased Random Walks on Bethe Lattices

EPL (Europhysics Letters) ◽

10.1209/0295-5075/13/7/002 ◽

1990 ◽

Vol 13 (7) ◽

pp. 583-586 ◽

Cited By ~ 4

Author(s):

D Cassi

Keyword(s):

Phase Transition ◽

Random Walks ◽

Dynamical Phase Transition ◽

Dynamical Phase ◽

Bethe Lattices ◽

Biased Random Walks

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Dynamical phase transitions and Loschmidt echo in the infinite-range XY model

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2015.0160 ◽

2016 ◽

Vol 374 (2069) ◽

pp. 20150160 ◽

Cited By ~ 36

Author(s):

Bojan Žunkovič ◽

Alessandro Silva ◽

Michele Fabrizio

Keyword(s):

Phase Transition ◽

Phase Transitions ◽

Order Parameter ◽

Quantum Systems ◽

Xy Model ◽

Time Behaviour ◽

Dynamical Phase ◽

Dynamical Phase Transitions ◽

Loschmidt Echo ◽

Infinite Range

We compare two different notions of dynamical phase transitions in closed quantum systems. The first is identified through the time-averaged value of the equilibrium-order parameter, whereas the second corresponds to non-analyticities in the time behaviour of the Loschmidt echo. By exactly solving the dynamics of the infinite-range XY model, we show that in this model non-analyticities of the Loschmidt echo are not connected to standard dynamical phase transitions and are not robust against quantum fluctuations. Furthermore, we show that the existence of either of the two dynamical transitions is not necessarily connected to the equilibrium quantum phase transition.

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DYNAMICAL THEORY OF PHASE TRANSITIONS AND COSMOLOGICAL EW AND QCD PHASE TRANSITIONS

Modern Physics Letters A ◽

10.1142/s0217732308027692 ◽

2008 ◽

Vol 23 (17n20) ◽

pp. 1325-1335

Author(s):

SANG PYO KIM

Keyword(s):

Phase Transition ◽

Phase Transitions ◽

Real Time ◽

Dynamical Theory ◽

Quench Rate ◽

Dynamical Phase ◽

Time Formalism ◽

Dynamical Phase Transitions ◽

Expansion Of The Universe ◽

The Universe

We critically review the cosmological EW and QCD phase transitions. The EW and QCD phase transitions would have proceeded dynamically since the expansion of the universe determines the quench rate and critical behaviors at the onset of phase transition slow down the phase transition. We introduce a real-time quench model for dynamical phase transitions and describe the evolution using a canonical real-time formalism. We find the correlation function, the correlation length and time and then discuss the cosmological implications of dynamical phase transitions on EW and QCD phase transitions in the early universe.

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Probing dynamical phase transitions with a superconducting quantum simulator

Science Advances ◽

10.1126/sciadv.aba4935 ◽

2020 ◽

Vol 6 (25) ◽

pp. eaba4935

Author(s):

Kai Xu ◽

Zheng-Hang Sun ◽

Wuxin Liu ◽

Yu-Ran Zhang ◽

Hekang Li ◽

...

Keyword(s):

Phase Transitions ◽

Quantum Limit ◽

Single Shot ◽

Many Body ◽

Dynamical Phase Transition ◽

Dynamical Phase ◽

Dynamical Phase Transitions ◽

Quantum Simulator ◽

Many Body Systems ◽

Loschmidt Echo

Nonequilibrium quantum many-body systems, which are difficult to study via classical computation, have attracted wide interest. Quantum simulation can provide insights into these problems. Here, using a programmable quantum simulator with 16 all-to-all connected superconducting qubits, we investigate the dynamical phase transition in the Lipkin-Meshkov-Glick model with a quenched transverse field. Clear signatures of dynamical phase transitions, merging different concepts of dynamical criticality, are observed by measuring the nonequilibrium order parameter, nonlocal correlations, and the Loschmidt echo. Moreover, near the dynamical critical point, we obtain a spin squeezing of −7.0 ± 0.8 dB, showing multipartite entanglement, useful for measurements with precision fivefold beyond the standard quantum limit. On the basis of the capability of entangling qubits simultaneously and the accurate single-shot readout of multiqubit states, this superconducting quantum simulator can be used to study other problems in nonequilibrium quantum many-body systems, such as thermalization, many-body localization, and emergent phenomena in periodically driven systems.

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