Dynamical quantum phase transitions in the one-dimensional extended Fermi–Hubbard model

Abstract

We study the emergence of dynamical quantum phase transitions (DQPTs) in a half-filled one-dimensional lattice described by the extended Fermi–Hubbard model, based on tensor network simulations. Considering different initial states, namely noninteracting, metallic, insulating spin and charge density waves, we identify several types of sudden interaction quenches which lead to DQPTs. Furthermore, clear connections to particular properties of observables, specifically the mean double occupation or charge imbalance, are established in two main regimes, and scenarios in which such correspondence is degraded and lost are discussed. Dynamical transitions resulting solely from high-frequency time-periodic modulation are also found, which are well described by a Floquet effective Hamiltonian. State-of-the-art cold-atom quantum simulators constitute ideal platforms to implement several reported DQPTs experimentally.

Scaling and universality at ramped quench dynamical quantum phase transitions

“…The concept of DQPT emanates from the analogy between the equilibrium partition function of a system, and Loschmidt amplitude, which measures the overlap between an initial state and its time-evolved one . As the equilibrium phase transition is signaled by non-analyticities in the thermal free energy, the DQPT is revealed through the nonanalytical behavior of dynamical free energy, where the real-time plays the role of the control parameter [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. DQPT displays a phase transition between dynamically emerging quantum phases, that takes place during the nonequilibrium coherent quantum time evolution under sudden/ramped quench or timeperiodic modulation of Hamiltonian [16,[85][86][87][88][89][90][91].…”

The singularities of the rate function of quantum coherent work in one-dimensional transverse field Ising model

“…One of the most intriguing examples of studying the dynamics of quantum many-body systems in this nonequilibrium thermodynamical formulation is dynamical phase transition [23][24][25]. There has been quite a remarkable amount of activity uncovering the features of dynamical phase transition in a range of physical models * xubm2018@163.com including Hermitian [25][26][27][28][29][30][31][32][33][34] and non-Hermitian [35][36][37] systems, topological matter [38][39][40][41][42][43][44][45][46][47][48], Floquet systems [49][50][51][52][53][54][55][56][57][58], and many-body localized systems [59][60][61], etc. Dynamical phase transition, manifested as real-time singularities in time-evolving quantum system after quenching a set of control parameters of its Hamiltonian, is indeed a dynamical analogue of equilibrium phase transition.…”

The singularities of the rate function of quantum coherent work in one-dimensional transverse field Ising model

“…One of the most intriguing examples of studying the dynamics of quantum many-body systems in this nonequilibrium thermodynamical formulation is dynamical phase transition [23][24][25]. There has been quite a remarkable amount of activity uncovering the features of dynamical phase transition in a range of physical models including Hermitian [25][26][27][28][29][30][31][32][33][34] and non-Hermitian [35][36][37] systems, topological matter [38][39][40][41][42][43][44][45][46][47][48], Floquet systems [49][50][51][52][53][54][55][56][57][58], and many-body localized systems [59][60][61], etc. Dynamical phase transition, manifested as real-time singularities in time-evolving quantum system after quenching a set of control parameters of its Hamiltonian, is indeed a dynamical analogue of equilibrium phase transition.…”