Integrability of open boundary driven quantum circuits

• URL: http://arxiv.org/abs/2406.12695v3
• Date: Sun, 06 Oct 2024 20:11:17 GMT
• Title: Integrability of open boundary driven quantum circuits
• Authors: Chiara Paletta, Tomaž Prosen,
• Abstract summary: We address the problem of Yang-Baxter integrability of double quantum circuit of qubits (spins 1/2) with open boundary conditions. We use this solution to build, from the transfer matrix formalism, integrable circuits with two step discrete time Floquet dynamics.
• Score: 0.0
• License:
• Abstract: In this paper, we address the problem of Yang-Baxter integrability of doubled quantum circuit of qubits (spins 1/2) with open boundary conditions where the two circuit replicas are only coupled at the left or right boundary. We investigate the cases where the bulk is given by elementary six vertex unitary gates of either the free fermionic XX type or interacting XXZ type. By using the Sklyanin's construction of reflection algebra, we obtain the most general solutions of the boundary Yang-Baxter equation for such a setup. We use this solution to build, from the transfer matrix formalism, integrable circuits with two step discrete time Floquet (aka brickwork) dynamics. We prove that, only if the bulk is a free-model, the boundary matrices are in general non-factorizable, and for particular choice of free parameters yield non-trivial unitary dynamics with boundary interaction between the two chains. Then, we consider the limit of continuous time evolution and we give the interpretation of a restricted set of the boundary terms in the Lindbladian setting. Specifically, for a particular choice of free parameters, the solutions correspond to an open quantum system dynamics with the source terms representing injecting or removing particles from the boundary of the spin chain.

Related papers

• Decoupling of External and Internal Dynamics in Driven Two-level Systems [49.96265870315999]
  We show how a laser driven two-level system can be decoupled into a set of equations acting only on the external degrees of freedom for each state. We give a way of characterizing the solvability of this family of problems by appealing to a classical oscillator with time-dependent damping. We show that chirping of the driving fields phase emerges naturally as a means of compensating the Ehrenfest/mean-value part of the detuning operator's dynamics.
  arXiv  Detail & Related papers  (2024-06-03T16:42:28Z)
• Duality between the quantum inverted harmonic oscillator and inverse square potentials [0.0]
  We show how the quantum mechanics of the inverted harmonic oscillator can be mapped to the quantum mechanics of a particle. We demonstrate this by relating both of these systems to the Berry-Keating system with hamiltonian $H=(xp+px)/2$. Our map does not require the boundary condition to be self-adjoint, as can be appropriate for systems that involve the absorption or emission of particles.
  arXiv  Detail & Related papers  (2024-02-21T16:24:16Z)
• Radiative transport in a periodic structure with band crossings [52.24960876753079]
  We derive the semi-classical model for the Schr"odinger equation in arbitrary spatial dimensions. We consider both deterministic and random scenarios. As a specific application, we deduce the effective dynamics of a wave packet in graphene with randomness.
  arXiv  Detail & Related papers  (2024-02-09T23:34:32Z)
• Exact finite-time correlation functions for multi-terminal setups: Connecting theoretical frameworks for quantum transport and thermodynamics [11.061707876645764]
  Transport in open quantum systems can be explored through various theoretical frameworks, including the quantum master equation, scattering matrix, and Heisenberg equation of motion. Existing literature treats these approaches independently, lacking a unified perspective. Our work addresses this gap by clarifying the role and status of these approaches using a minimal single-level quantum dot model in a two-terminal setup.
  arXiv  Detail & Related papers  (2023-12-22T21:09:18Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Quantum Reference Frames at the Boundary of Spacetime [0.0]
  An analysis is given of the local phase space of gravity coupled to matter to second order in perturbation theory. The boundary modes take the role of reference frames for both diffeomorphisms and internal Lorentz rotations. A multi-fingered Schr"odinger equation determines the relational evolution of the quantum states in the bulk.
  arXiv  Detail & Related papers  (2023-02-22T20:10:03Z)
• The Floquet Baxterisation [0.36448362316632116]
  We construct a generic framework for integrable quantum circuits using Floquet Baxterisation. We demonstrate the dynamical anti-unitary symmetry breaking in the easy-plane regime.
  arXiv  Detail & Related papers  (2022-06-30T09:18:07Z)
• The frustration-free fully packed loop model [4.965221313169878]
  We consider a quantum fully packed loop model on the square lattice with a frustration-free projector Hamiltonian and ring-exchange interactions acting on plaquettes. We discuss how the boundary term fractures the Hilbert space into Krylov subspaces, and we prove that the Hamiltonian is ergodic within each subspace. We show that the spectrum is shown to be gapless in the thermodynamic limit with a trial state constructed by adding a twist to the ground state superposition.
  arXiv  Detail & Related papers  (2022-06-03T18:00:04Z)
• 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)
• Lifting the Convex Conjugate in Lagrangian Relaxations: A Tractable Approach for Continuous Markov Random Fields [53.31927549039624]
  We show that a piecewise discretization preserves better contrast from existing discretization problems. We apply this theory to the problem of matching two images.
  arXiv  Detail & Related papers  (2021-07-13T12:31:06Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)

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.