Complexity and Floquet dynamics: non-equilibrium Ising phase transitions

• URL: http://arxiv.org/abs/2009.00069v1
• Date: Mon, 31 Aug 2020 19:13:03 GMT
• Title: Complexity and Floquet dynamics: non-equilibrium Ising phase transitions
• Authors: Giancarlo Camilo and Daniel Teixeira
• Abstract summary: We study the time-dependent circuit complexity of the periodically driven transverse field Ising model. In the high-frequency driving limit the system is known to exhibit non-equilibrium phase transitions governed by the amplitude of the driving field.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the time-dependent circuit complexity of the periodically driven transverse field Ising model using Nielsen's geometric approach. In the high-frequency driving limit the system is known to exhibit non-equilibrium phase transitions governed by the amplitude of the driving field. We analytically compute the complexity in this regime and show that it clearly distinguishes between the different phases, exhibiting a universal linear behavior at early times. We also evaluate the time averaged complexity, provide evidence of non-analytic behavior at the critical points, and discuss its origin. Finally, we comment on the freezing of quantum dynamics at specific configurations and on the use of complexity as a new tool to understand quantum phase transitions in Floquet systems.

Related papers

• Universal Early-Time Growth in Quantum Circuit Complexity [0.0]
  We show that quantum circuit complexity for the unitary time evolution operator of any time-independent Hamiltonian is bounded by linear growth at early times. We are able to extract the early-time behavior and dependence on the lattice spacing of complexity of field theories in the limit, demonstrating how this approach applies to systems that have been previously difficult to study using existing techniques for quantum circuit complexity.
  arXiv  Detail & Related papers  (2024-06-18T18:27:36Z)
• Anomalous Floquet Phases. A resonance phenomena [0.0]
  Floquet topological phases emerge when systems are periodically driven out-of-equilibrium. We show that resonances in Floquet phases can be accurately captured in analytical terms. We also find a bulk-to-boundary correspondence between the number of edge states in finite systems.
  arXiv  Detail & Related papers  (2023-12-11T19:00:13Z)
• Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution [44.99833362998488]
  We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate quantum systems classically. We prove that the most used scheme, the time-dependent Variational Monte Carlo (tVMC), is affected by a systematic statistical bias. We show that a different scheme based on the solution of an optimization problem at each time step is free from such problems.
  arXiv  Detail & Related papers  (2023-05-23T17:38:10Z)
• Quantifying spatio-temporal patterns in classical and quantum systems out of equilibrium [0.0]
  A rich variety of non-equilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques. By the example of the discrete time crystal realized in non-equilibrium quantum systems we provide a complete low-level characterization of this nontrivial dynamical phase with only processing bitstrings.
  arXiv  Detail & Related papers  (2023-02-28T13:27:45Z)
• Out-of-time-order correlator in the quantum Rabi model [62.997667081978825]
  We show that out-of-time-order correlator derived from the Loschmidt echo signal quickly saturates in the normal phase. We show that the effective time-averaged dimension of the quantum Rabi system can be large compared to the spin system size.
  arXiv  Detail & Related papers  (2022-01-17T10:56:57Z)
• Complex time method for quantum dynamics when an exceptional point is encircled in the parameter space [0.0]
  We revisit the complex time method for the application to quantum dynamics as an exceptional point is encircled in the parameter space of the Hamiltonian. We discuss a switch between Rabi oscillations and rapid adiabatic passage which occurs upon the encircling of an exceptional point in a special time-symmetric case.
  arXiv  Detail & Related papers  (2021-10-27T14:41:44Z)
• 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)
• Determination of dynamical quantum phase transitions in strongly correlated many-body systems using Loschmidt cumulants [0.0]
  We use Loschmidt cumulants to determine the critical times of interacting quantum systems after a quench. Our work demonstrates that Loschmidt cumulants are a powerful tool to unravel the far-from-equilibrium dynamics of strongly correlated many-body systems.
  arXiv  Detail & Related papers  (2020-11-27T09:03:47Z)
• Universality of entanglement transitions from stroboscopic to continuous measurements [68.8204255655161]
  We show that the entanglement transition at finite coupling persists if the continuously measured system is randomly nonintegrable. This provides a bridge between a wide range of experimental settings and the wealth of knowledge accumulated for the latter systems.
  arXiv  Detail & Related papers  (2020-05-04T21:45:59Z)
• Unsupervised machine learning of quantum phase transitions using diffusion maps [77.34726150561087]
  We show that the diffusion map method, which performs nonlinear dimensionality reduction and spectral clustering of the measurement data, has significant potential for learning complex phase transitions unsupervised. This method works for measurements of local observables in a single basis and is thus readily applicable to many experimental quantum simulators.
  arXiv  Detail & Related papers  (2020-03-16T18:40:13Z)

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.