Insights from the exact analytical solution of periodically driven transverse field Ising chain

• URL: http://arxiv.org/abs/2409.08830v2
• Date: Wed, 29 Jan 2025 07:05:26 GMT
• Title: Insights from the exact analytical solution of periodically driven transverse field Ising chain
• Authors: Pritam Das, Anirban Dutta,
• Abstract summary: We derive an exact analytical expression at stroboscopic intervals for the time-dependent wave function of a class of integrable quantum many-body systems. To investigate long-time dynamics, we use the wave function to obtain an exact analytical expression for the expectation values of the defect density, magnetization, residual energy, fidelity, and the correlation function after the $n$th drive cycle.
• Score: 1.450261153230204
• License:
• Abstract: We derive an exact analytical expression at stroboscopic intervals for the time-dependent wave function of a class of integrable quantum many-body systems, driven by the periodic delta-kick protocol. To investigate long-time dynamics, we use the wave function to obtain an exact analytical expression for the expectation values of the defect density, magnetization, residual energy, fidelity, and the correlation function after the $n$th drive cycle. Periodically driven integrable closed quantum systems absorb energy, and the long-time universal dynamics are described by the periodic generalized Gibbs ensemble (GGE). We demonstrate that the expectation values of all observables are divided into two parts: one highly oscillatory term that depends on the drive cycle n, and the rest of the terms are independent of it. Typically, the $n$-independent part constitutes the saturation at large n and periodic GGE. The contribution from the highly oscillatory term vanishes in large $n$. We also generalize our formalism to include square pulse and sinusoidal driving protocols.

Related papers

• Powering a quantum clock with a non-equilibrium steady state [50.24983453990065]
  We propose powering a quantum clock with the non-thermal resources offered by the stationary state of an integrable quantum spin chain. Using experimentally relevant examples of quantum spin chains, we suggest crossing a phase transition point is crucial for optimal performance.
  arXiv  Detail & Related papers  (2024-12-17T17:25:11Z)
• Exactly solvable dynamics and signatures of integrability in an infinite-range many-body Floquet spin system [0.6345523830122168]
  We study $N$ qubits having infinite-range Ising interaction and subjected to periodic pulse of external magnetic field. We solve the cases of $N=5$ to $11$ qubits analytically, finding its eigensystem, the dynamics of the entanglement for various initial states, and the unitary evolution operator.
  arXiv  Detail & Related papers  (2023-07-26T11:41:52Z)
• Independent-oscillator model and the quantum Langevin equation for an oscillator: A review [19.372542786476803]
  A derivation of the quantum Langevin equation is outlined based on the microscopic model of the heat bath. In the steady state, we analyze the quantum counterpart of energy equipartition theorem. The free energy, entropy, specific heat, and third law of thermodynamics are discussed for one-dimensional quantum Brownian motion.
  arXiv  Detail & Related papers  (2023-06-05T07:59:35Z)
• Initial value formulation of a quantum damped harmonic oscillator [0.18416014644193066]
  We study the initial state-dependence, decoherence, and thermalization of a quantum damped harmonic oscillator. We find that the dynamics must include a non-vanishing noise term to yield physical results for the purity. We briefly consider time-nonlocal dissipation as well, to show that the fluctuation-dissipation relation is satisfied for a specific choice of dissipation kernels.
  arXiv  Detail & Related papers  (2023-03-08T19:03:12Z)
• Indication of critical scaling in time during the relaxation of an open quantum system [34.82692226532414]
  Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation length, universal power-law scaling behavior with critical exponents independent of microscopic system details is found.
  arXiv  Detail & Related papers  (2022-08-10T05:59:14Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor [80.17270167652622]
  Quantum-body systems display rich phase structure in their low-temperature equilibrium states. We experimentally observe an eigenstate-ordered DTC on superconducting qubits. Results establish a scalable approach to study non-equilibrium phases of matter on current quantum processors.
  arXiv  Detail & Related papers  (2021-07-28T18:00:03Z)
• Stochastic Path Integral Analysis of the Continuously Monitored Quantum Harmonic Oscillator [0.0]
  We deduce the evolution equations for position and momentum expectation values and the covariance matrix elements from the system's characteristic function. Our results provide insights into the time dependence of the system during the measurement process, motivating their importance for quantum measurement engine/refrigerator experiments.
  arXiv  Detail & Related papers  (2021-03-10T15:04:49Z)
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation [58.720142291102135]
  Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation. We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH) We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
  arXiv  Detail & Related papers  (2021-03-01T17:51:46Z)
• Restoring coherence via aperiodic drives in a many-body quantum system [0.0]
  We study the unitary dynamics of randomly or quasi-periodically driven tilted Bose-Hubbard (tBH) model in one dimension deep inside its Mott phase. We show that starting from a regime where the periodic drive leads to rapid thermalization, a random drive, which consists of a random sequence of square pulses with period $T+alpha dT$, restores coherent oscillations for special values of $dT$. A similar phenomenon can be seen for a quasi-periodic drive following a Thue-Morse sequence where such coherent behavior is shown to occur for a larger number of points in the $
  arXiv  Detail & Related papers  (2020-02-20T11:33:13Z)
• Many-Body Dephasing in a Trapped-Ion Quantum Simulator [0.0]
  How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. We analyse and observe the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator.
  arXiv  Detail & Related papers  (2020-01-08T12:33:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.