Determination of dynamical quantum phase transitions in strongly correlated many-body systems using Loschmidt cumulants

Abstract

Dynamical phase transitions extend the notion of criticality to non-stationary settings and are characterized by sudden changes in the macroscopic properties of time-evolving quantum systems. Investigations of dynamical phase transitions combine aspects of symmetry, topology, and non-equilibrium physics, however, progress has been hindered by the notorious difficulties of predicting the time evolution of large, interacting quantum systems. Here, we tackle this outstanding problem by determining the critical times of interacting many-body systems after a quench using Loschmidt cumulants. Specifically, we investigate dynamical topological phase transitions in the interacting Kitaev chain and in the spin-1 Heisenberg chain. To this end, we map out the thermodynamic lines of complex times, where the Loschmidt amplitude vanishes, and identify the intersections with the imaginary axis, which yield the real critical times after a quench. For the Kitaev chain, we can accurately predict how the critical behavior is affected by strong interactions, which gradually shift the time at which a dynamical phase transition occurs. We also discuss the experimental perspectives of predicting the first critical time of a quantum many-body system by measuring the energy fluctuations in the initial state, and we describe the prospects of implementing our method on a near-term quantum computer with a limited number of qubits. Our work demonstrates that Loschmidt cumulants are a powerful tool to unravel the far-from-equilibrium dynamics of strongly correlated many-body systems, and our approach can immediately be applied in higher dimensions.

arXiv comment9+5 pages, 4 figures

References in corpus (56)

• Atomic quantum gases in periodically driven optical lattices
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Dynamical quantum phase transitions: a review
• Time-evolution methods for matrix-product states
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Observation of a dynamical topological phase transition
• Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
• Universal oscillations in counting statistics
• Dynamical Topological Order Parameters far from Equilibrium
• Ground State Phase Diagram of S=1 XXZ Chains with Uniaxial Single-Ion-Type Anisotropy
• Dynamical phase transitions after quenches in non-integrable models
• Dynamical quantum phase transitions: scaling and universality
• Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach
• Topological classification of dynamical phase transitions
• Disentangling dynamical phase transitions from equilibrium phase transitions
• Simulating dynamic quantum phase transitions in photonic quantum walks
• Real- and imaginary-time evolution with compressed quantum circuits
• Dynamical phase diagram of spin chains with long-range interactions
• Colloquium: Atomic spin chains on surfaces
• Detecting equilibrium and dynamical quantum phase transitions in Ising chains via out-of-time-ordered correlators
• Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism
• Probing the dynamical phase transition with a superconducting quantum simulator
• Anomalous dynamical phase in quantum spin chains with long-range interactions
• Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model
• Observation of dynamical quantum phase transition by a superconducting qubit simulation
• Observation of Dynamical Quantum Phase Transition with Correspondence in Excited State Phase Diagram
• Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution
• Quenches and dynamical phase transitions in a non-integrable quantum Ising model
• Trajectory phase transitions, Lee-Yang zeros, and high-order cumulants in full counting statistics
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Experimental Determination of Dynamical Lee-Yang Zeros
• Quench dynamics and zero-energy modes: the case of the Creutz model
• Dynamical free energy and the Loschmidt-echo for a class of quantum quenches in the Heisenberg spin chain
• The Lee-Yang theory of equilibrium and nonequilibrium phase transitions
• Probing the anomalous dynamical phase in long-range quantum spin chains through Fisher-zero lines
• Floquet dynamical quantum phase transition in the extended XY model: nonadiabatic to adiabatic topological transition
• A bulk-boundary correspondence for dynamical phase transitions in one-dimensional topological insulators and superconductors
• Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems
• Dynamical quantum phase transitions in $U(1)$ quantum link models
• Observation of dynamical phase transitions in a topological nanomechanical system
• Dynamical Quantum Phase Transitions in Systems with Continuous Symmetry Breaking
• Quasiparticle origin of dynamical quantum phase transitions
• Dynamical criticality and domain-wall coupling in long-range Hamiltonians
• Emergent Glassy Dynamics in a Quantum Dimer Model
• Lee-Yang zeros and large-deviation statistics of a molecular zipper
• Dynamical topological quantum phase transitions in nonintegrable models
• Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model
• Determination of universal critical exponents using Lee-Yang theory
• Dynamical quantum phase transitions in collapse and revival oscillations of a quenched superfluid
• Controlling Dynamical Quantum Phase Transitions
• High cumulants in the counting statistics measured for a quantum dot
• Lee-Yang theory of the Curie-Weiss model and its rare fluctuations
• Return amplitude after a quantum quench in the XY chain
• Odd thermodynamic limit for the Loschmidt echo
• Geometrical quench and dynamical quantum phase transition in the $\alpha -T_3$ lattice

Cited by in corpus (14)

• Dissipative Floquet Dynamical Quantum Phase Transition
• Engineering Floquet Dynamical Quantum Phase Transition
• Dynamical quantum phase transitions in a spinor Bose-Einstein condensate and criticality enhanced quantum sensing
• Yang-Lee Zeros, Semicircle Theorem, and Nonunitary Criticality in Bardeen-Cooper-Schrieffer Superconductivity
• Lee-Yang theory of the two-dimensional quantum Ising model
• Interaction-driven dynamical quantum phase transitions in a strongly correlated bosonic system
• Mechanism of dynamical phase transitions: The complex-time survival amplitude
• Metamorphic dynamical quantum phase transition in double-quench processes at finite temperatures
• Lee-Yang theory of Bose-Einstein condensation
• Late-time critical behavior of local string-like observables under quantum quenches
• Lee-Yang theory of quantum phase transitions with neural network quantum states
• Dynamical quantum phase transitions from random matrix theory
• Dynamical detection of mean-field topological phases in an interacting Chern insulator
• Dynamical quantum phase transitions in strongly correlated two-dimensional spin lattices following a quench