Effect of long-range hopping on dynamic quantum phase transitions of an exactly solvable free-fermion model: Nonanalyticities at almost all times

Abstract

In this work, we investigate quenches in a free-fermion chain with long-range hopping which decay with the distance with an exponent $\nu$ and has range $D$. By exploring the exact solution of the model, we found that the dynamic free energy is non-analytical, in the thermodynamic limit, whenever the sudden quench crosses the equilibrium quantum critical point. We were able to determine the non-analyticities of dynamic free energy $f(t)$ at some critical times $t^c$ by solving nonlinear equations. We also show that the Yang-Lee-Fisher (YLF) zeros cross the real-time axis at those critical times. We found that the number of nontrivial critical times, $N_s,$ depends on $\nu$ and $D$. In particular, we show that for small $\nu$ and large $D$ the dynamic free energy presents non-analyticities in any time interval $\Delta t\sim 1/D\ll 1$, i.e., there are \emph{non-analyticities at almost all times}. For the spacial case $\nu =0$, we obtain the critical times in terms of a simple expression of the model parameters and also show that $f(t)$ is non-analytical even for finite system under anti-periodic boundary condition, when we consider some special values of quench parameters. We also show that, generically, the first derivative of the dynamic free energy is discontinuous at the critical time instant when the YLF zeros are non-degenerate. On the other hand, when they become degenerate, all derivatives of $f(t)$ exist at the associated critical instant.

arXiv comment11 pages, 7 figures, 1 table, final version

References in corpus (33)

• Continuous Quantum Phase Transitions
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Effective quantum spin systems with ion traps
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Dynamical quantum phase transitions: a review
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Emergence and Frustration of Magnetic Order with Variable-Range Interactions in a Trapped Ion Quantum Simulator
• 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
• Dynamical phase transitions after quenches in non-integrable models
• 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
• Boundary energy and boundary states in integrable quantum field theories
• Observation of Lee-Yang zeros
• Dynamical phase diagram of spin chains with long-range interactions
• Anomalous dynamical phase in quantum spin chains with long-range interactions
• First order dynamical phase transitions
• Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model
• Observation of dynamical quantum phase transition by a superconducting qubit simulation
• Observing emergent hydrodynamics in a long-range quantum magnet
• Probing Lee-Yang zeros and coherence sudden death
• Probing the role of long-range interactions in the dynamics of a long-range Kitaev Chain
• Quench dynamics and zero-energy modes: the case of the Creutz model
• Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
• Probing the anomalous dynamical phase in long-range quantum spin chains through Fisher-zero lines
• Dynamical Quantum Phase Transition and Quasi Particle Excitation
• Dynamical quantum phase transitions in discrete time crystals
• Out-of-equilibrium phase diagram of long-range superconductors
• Dynamical criticality and domain-wall coupling in long-range Hamiltonians
• Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions
• Disorder-induced dynamical Griffiths singularities after certain quantum quenches

Cited by in corpus (1)

• Competition of long-range interactions and noise at ramped quench dynamical quantum phase transition: The case of the long-range pairing Kitaev chain