Distinction Between Transport and R\'enyi Entropy Growth in Kinetically Constrained Models

• URL: http://arxiv.org/abs/2208.07480v1
• Date: Tue, 16 Aug 2022 00:34:18 GMT
• Title: Distinction Between Transport and R\'enyi Entropy Growth in Kinetically Constrained Models
• Authors: Zhi-Cheng Yang
• Abstract summary: We study two types of U(1)-symmetric quantum circuits with XNOR and Fredkin constraints. We find numerically that while spin transport in both models is subdiffusive, the second R'enyi entropy grows diffusively in the XNOR model. Our results suggest that care must be taken when relating transport and entanglement entropy dynamics in generic quantum systems with conservation laws.
• Score: 1.9087335681007476
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Conservation laws and the associated hydrodynamic modes have important consequences on the growth of higher R\'enyi entropies in isolated quantum systems. It has been shown in various random unitary circuits and Hamiltonian systems that the dynamics of the R\'enyi entropies in the presence of a U(1) symmetry obey $S^{(n\geq 2)}(t) \propto t^{1/z}$, where $z$ is identified as the dynamical exponent characterizing transport of the conserved charges. Here, however, we demonstrate that this simple identification may not hold in certain quantum systems with kinetic constraints. In particular, we study two types of U(1)-symmetric quantum automaton circuits with XNOR and Fredkin constraints, respectively. We find numerically that while spin transport in both models is subdiffusive, the second R\'enyi entropy grows diffusively in the XNOR model, and superdiffusively in the Fredkin model. For systems with XNOR constraint, this distinction arises since the spin correlation function can be attributed to an emergent tracer dynamics of tagged particles, whereas the R\'enyi entropies are constrained by collective transport of the particles. Our results suggest that care must be taken when relating transport and entanglement entropy dynamics in generic quantum systems with conservation laws.

Related papers

• Anomalous transport in U(1)-symmetric quantum circuits [41.94295877935867]
  Investigation of discrete-time transport in a generic U(1)-symmetric disordered model tuned across an array of different dynamical regimes. We develop an aggregate quantity, a circular statistical moment, which is a simple function of the magnetization profile. From this quantity we extract transport exponents, revealing behaviors across the phase diagram consistent with localized, diffusive, and - most interestingly for a disordered system - superdiffusive regimes.
  arXiv  Detail & Related papers  (2024-11-21T17:56:26Z)
• Quantum many-body spin ratchets [0.0]
  We show that breaking of space-reflection symmetry results in a drift in the dynamical spin susceptibility. We also show that the scaled cumulant generating function of the time-integrated current instead obeys a generalized fluctuation relation.
  arXiv  Detail & Related papers  (2024-06-03T17:51:36Z)
• Emergent Anomalous Hydrodynamics at Infinite Temperature in a Long-Range XXZ Model [14.297989605089663]
  We find anomalous hydrodynamics in a spin-1/2 XXZ chain with power-law couplings. We quantify the degree of quantum chaos using the Kullback-Leibler divergence. This work offers another deep understanding of emergent anomalous transport phenomena in a wider range of non-integrable quantum many-body systems.
  arXiv  Detail & Related papers  (2024-03-26T17:50:04Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states [11.04121146441257]
  We prove that the entanglement entropy of any pure initial state of a bosonic quantum system grows linearly in time. We discuss several applications of our results to physical systems with (weakly) interacting Hamiltonians and periodically driven quantum systems.
  arXiv  Detail & Related papers  (2021-07-23T07:55:38Z)
• Quantum critical systems with dissipative boundaries [0.0]
  We study the effects of dissipative boundaries in many-body systems at continuous quantum transitions. As paradigmatic models, we consider fermionic wires subject to dissipative interactions at the boundaries.
  arXiv  Detail & Related papers  (2021-06-04T15:08:06Z)
• Statistical mechanics of one-dimensional quantum droplets [0.0]
  We study the dynamical relaxation process of modulationally unstable one-dimensional quantum droplets. We find that the instability leads to the spontaneous formation of quantum droplets featuring multiple collisions.
  arXiv  Detail & Related papers  (2021-02-25T15:30:30Z)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)
• Quantum criticality in the nonunitary dynamics of $(2+1)$-dimensional free fermions [5.691318972818067]
  We show that the obtained steady state is critical regardless the strength of the nonunitary evolution. Numerical results indicate that the entanglement entropy has a logarithmic violation of the area-law.
  arXiv  Detail & Related papers  (2021-01-12T06:56:24Z)

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.