Light-Cone and Diffusive Propagation of Correlations in a Many-Body Dissipative System

Bernier, Jean-Sébastien; Tan, Ryan; Bonnes, Lars; Guo, Chu; Poletti, Dario; Kollath, Corinna

doi:10.1103/physrevlett.120.020401

Cited by 37 publications

(34 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition to the equilibrium physics of the model, the investigation of dynamical processes, arising from tuning * werner.weiss@uni-ulm.de the system's parameters, are of great interest [28][29][30][31][32][33], especially towards engineering complex phases in quantum gases. An important scenario in this context are quasi-adiabatic quenches across quantum phase transitions, for which the Kibble-Zurek hypothesis [34][35][36][37] offers a simple and intuitive theoretical framework, yet allowing for a quantitative understanding of the formation of defects when crossing a quantum critical point.…”

Section: Introductionmentioning

confidence: 99%

Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures

et al. 2018

View full text Add to dashboard Cite

We use tensor network methods -Matrix Product States, Tree Tensor Networks, and Locally Purified Tensor Networks -to simulate the one-dimensional Bose-Hubbard model for zero and finite temperatures in experimentally accessible regimes. We first explore the effect of thermal fluctuations on the system ground state by characterizing its Mott and superfluid features. Then, we study the behavior of the out-of-equilibrium dynamics induced by quenches of the hopping parameter. We confirm a Kibble-Zurek scaling for zero temperature and characterize the finite temperature behavior, which we explain by means of a simple argument.

show abstract

Section: Introductionmentioning

confidence: 99%

Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures

et al. 2018

View full text Add to dashboard Cite

show abstract

“…in contact with an environment) evaluating out-of-equilibrium two-time correlations has proven extremely challenging. Most works have instead focused on characterizing the non-equilibrium dynamics of open systems by considering the universal scaling behavior of simpler observables or the propagation of single-time correlations [8,9], by using various approximate approaches to evaluate two-time correlations [10][11][12][13][14][15], or by considering small many-body quantum systems [16].Here, for the first time, we evaluate quasi-exactly the evolution of both the two-time correlations along the zspin direction, S z l (t 2 )S z l+d (t 1 ) , and along the ±-spin directions, S + l (t 2 )S − l+d (t 1 ) , in a quantum XXZ spin-1/2 chain in contact with a memoryless environment causing dephasing. S z l and S ± l are the spin-1/2 operators in the z and ± directions at site l. Previous works on this system had solely focused on the evaluation of equal-time correlations along the ±-spin directions [17] identifying an algebraic regime similar to the one found for interacting bosons in contact with a dissipative environment causing dephasing [18,19].…”

mentioning

confidence: 99%

Evolution of two-time correlations in dissipative quantum spin systems: Aging and hierarchical dynamics

et al. 2019

Self Cite

View full text Add to dashboard Cite

We consider the evolution of two-time correlations in the quantum XXZ spin-chain in contact with an environment causing dephasing. Extending quasi-exact time-dependent matrix product state techniques to consider the dynamics of two-time correlations within dissipative systems, we uncover the full quantum behavior for these correlations along all spin directions. Together with insights from adiabatic elimination and kinetic Monte Carlo, we identify three dynamical regimes. For initial times, their evolution is dominated by the system unitary dynamics and depends on the initial state and the Hamiltonian parameters. For weak spin-spin interaction anisotropy, after this initial dynamical regime, two-time correlations enter an algebraic scaling regime signaling the breakdown of time-translation invariance and the emergence of aging. For stronger interaction anisotropy, these correlations first go through a stretched exponential regime before entering the algebraic one. Such complex relaxation arises due to the competition between the proliferation dynamics of energetically costly excitations and their motion. As a result, dissipative heating dynamics of spin systems can be used to probe the entire spectrum of the underlying Hamiltonian.Two-time correlations are powerful tools to capture the fundamental dynamical features of many-body systems both in and away from equilibrium. These correlation functions are of the form B(t 2 )A(t 1 ) where A and B are operators, t 1 and t 2 are two different times, and . . . = tr(ρ . . . ) is the average over the density matrix ρ of a given system. Numerous experimental techniques have been developed to probe these correlations measuring the response of many-body systems. A non-exhaustive list includes ARPES [1], neutron scattering [2] or conductivity and magnetization measurements in solids [3], and radiofrequency [4], Raman, Bragg [5] (and references therein) or modulation spectroscopy [6] in cold gases. In equilibrium, these experimental methods provide information on various spectral features such as collective excitations and bound states. Whereas away from equilibrium, these techniques are employed to identify the formation of dynamically induced states in isolated quantum systems subjected to an external parameter change, and to capture, using for example magnetic susceptibility measurements, the aging dynamics of classical spin glasses [7].Theoretically, two-time correlations have been studied in isolated many-body quantum systems (i.e. not in contact with an environment), both in and far from equilibrium. However, for open many-body quantum systems (i.e. in contact with an environment) evaluating out-of-equilibrium two-time correlations has proven extremely challenging. Most works have instead focused on characterizing the non-equilibrium dynamics of open systems by considering the universal scaling behavior of simpler observables or the propagation of single-time correlations [8,9], by using various approximate approaches to evaluate two-time correlations [10][11][12][13][14...

show abstract

“…The left-most panel in Fig. 1(c) plots an equal-time correlation C(l, t) = Tr[ρ(t)ĉ † lĉ 0 ], which exhibits a blurred light cone [93]. Since the Liouvillian of Eq.…”

mentioning

confidence: 99%

Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations

Ashida

Ueda

2018

Phys. Rev. Lett.

View full text Add to dashboard Cite

The ability to measure single quanta allows the complete characterization of small quantum systems known as full-counting statistics. Quantum gas microscopy enables one to observe many-body systems at the single-atom precision. We extend the idea of full-counting statistics to nonequilibrium open many-particle dynamics and apply it to discuss the quench dynamics. By way of illustration, we consider an exactly solvable model to demonstrate the emergence of unique phenomena such as nonlocal and chiral propagation of correlations, leading to a concomitant oscillatory entanglement growth. We find that correlations can propagate beyond the conventional maximal speed, known as the Lieb-Robinson bound, at the cost of probabilistic nature of quantum measurement. These features become most prominent at the real-to-complex spectrum transition point of an underlying parity-time-symmetric effective non-Hermitian Hamiltonian. A possible experimental situation with quantum gas microscopy is discussed.

show abstract

Light-Cone and Diffusive Propagation of Correlations in a Many-Body Dissipative System

Cited by 37 publications

References 36 publications

Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures

Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures

Evolution of two-time correlations in dissipative quantum spin systems: Aging and hierarchical dynamics

Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations

Contact Info

Product

Resources

About