Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model

Abstract

We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of non-analyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of ${\mathbb{Z}}_2$ symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.

journal article, 15 pages, 12 figures. Final version

References in corpus (23)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Probing many-body dynamics on a 51-atom quantum simulator
• Dynamical quantum phase transitions: a review
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Mixed-state fidelity and quantum criticality at finite temperature
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model and proposed realization in optical cavity QED
• Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose-Hubbard model
• Nonthermal antiferromagnetic order and nonequilibrium criticality in the Hubbard model
• Mixed state dynamical quantum phase transition and emergent topology
• Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point
• Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition
• Exact infinite-time statistics of the Loschmidt echo for a quantum quench
• Probing the anomalous dynamical phase in long-range quantum spin chains through Fisher-zero lines
• Exploring dynamical phase transitions and prethermalization with quantum noise of excitations
• Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics
• Dynamical Quantum Phase Transitions in Systems with Continuous Symmetry Breaking
• Dynamical quantum phase transitions in the quantum Potts chain
• The fate of dynamical phase transitions at finite temperatures and in open systems
• Prethermalization from a low-density Holstein-Primakoff expansion

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