Dynamical quantum phase transition in a bosonic system with long-range interactions

Abstract

In this paper, we investigate the dynamical quantum phase transitions appearing in the Loschmidt echo and the time-dependent order parameter of a quantum system of harmonically coupled degenerate bosons as a function of the power-law decay $\sigma$ of long-range interactions. Following a sudden quench, the nonequilibrium dynamics of this system are governed by a set of nonlinear coupled Ermakov equations. To solve them, we develop an analytical approximation valid at late times. Based on this approximation, we show that the emergence of a dynamical quantum phase transition hinges on the generation of a finite mass gap following the quench, starting from a massless initial state. In general, we can define two distinct dynamical phases characterized by the finiteness of the post-quench mass gap. The Loschmidt echo exhibits periodical nonanalytic cusps whenever the initial state has a vanishing mass gap and the final state has a finite mass gap. These cusps are shown to coincide with the maxima of the time-dependent long-range correlations.

10 pages, 5 figures

References in corpus (46)

• Nonequilibrium dynamics of closed interacting quantum systems
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Relaxation and Pre-thermalization in an Isolated Quantum System
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Dynamical phase transition in correlated fermionic lattice systems
• Local emergence of thermal correlations in an isolated quantum many-body system
• Coupling Identical 1D Many-Body Localized Systems
• Periodically Driving a Many-Body Localized Quantum System
• Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
• Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems
• Dynamical quantum phase transitions: scaling and universality
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• Topological classification of dynamical phase transitions
• Disentangling dynamical phase transitions from equilibrium phase transitions
• Exploring dynamical phase transitions with cold atoms in an optical cavity
• Dynamical quantum phase transitions in systems with broken-symmetry phases
• Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
• Dynamical phase diagram of spin chains with long-range interactions
• Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose-Hubbard model
• Quantum quench in interacting field theory: a self-consistent approximation
• Anomalous dynamical phase in quantum spin chains with long-range interactions
• Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model
• Criticality and Phase Diagram of Quantum Long-Range $\text{O(N)}$ models
• Dynamical Quantum Phase Transitions: A Geometric Picture
• Probing the role of long-range interactions in the dynamics of a long-range Kitaev Chain
• Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model
• Fixed Points Structure & Effective Fractional Dimension for O(N) Models with Long-Range Interactions
• On equilibration and coarsening in the quantum O(N) model at infinite $N$
• Dynamical free energy and the Loschmidt-echo for a class of quantum quenches in the Heisenberg spin chain
• Dynamical critical scaling of long-range interacting quantum magnets
• Dynamical quantum phase transitions: a brief survey
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Criticality revealed through quench dynamics the Lipkin-Meshkov-Glick model
• Out-of-equilibrium phase diagram of long-range superconductors
• Dynamical Quantum Phase Transitions in Systems with Continuous Symmetry Breaking
• Quasiparticle origin of dynamical quantum phase transitions
• New dynamical scaling universality for quantum networks across adiabatic quantum phase transitions
• Criticality of Spin Systems with Weak Long-Range Interactions
• Dynamical criticality and domain-wall coupling in long-range Hamiltonians
• Time-evolution and dynamical phase transitions at a critical time in a system of one dimensional bosons after a quantum quench
• One-dimensional long-range percolation: a numerical study
• Dynamical Topological Phase Transition in a Bose-Einstein Condensate
• Dynamical quantum phase transition in a system of non-interacting bosons
• Universal dynamical scaling of long-range topological superconductors

Cited by in corpus (15)

• Long-range interacting quantum systems
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Metastability and discrete spectrum of long-range systems
• Finite temperature dynamical quantum phase transition in a non-Hermitian system
• Anomaly in dynamical quantum phase transition in non-Hermitian system with extended gapless phases
• Dynamical Quantum Phase Transitions Following Double Quenches: Persistence of the Initial State vs Dynamical Phases
• Competition of long-range interactions and noise at ramped quench dynamical quantum phase transition: The case of the long-range pairing Kitaev chain
• Dynamical quantum phase transitions in the one-dimensional extended Fermi-Hubbard model
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Persistent anomaly in dynamical quantum phase transition in long-range non-Hermitian $p$-wave Kitaev chain
• Entanglement propagation and dynamics in non-additive quantum systems
• Complex scaling flows in the quench dynamics of interacting particles
• Universal scaling at a pre-thermal dark state
• Dynamical quantum phase transitions in Stark quantum spin chains
• Loschmidt echo and Momentum Distribution in a Kitaev Spin Chain