Quantum complexity and topological phases of matter

• URL: http://arxiv.org/abs/2205.05688v3
• Date: Tue, 8 Nov 2022 08:15:20 GMT
• Title: Quantum complexity and topological phases of matter
• Authors: Pawel Caputa, Sinong Liu
• Abstract summary: We find that the complexity of quantum many-body states, defined as a spread, may serve as a new probe that distinguishes topological phases of matter. We illustrate this analytically in one of the representative examples, the Su-Schrieffer-Heeger model, finding that spread complexity becomes constant in the topological phase.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: In this work, we find that the complexity of quantum many-body states, defined as a spread in the Krylov basis, may serve as a new probe that distinguishes topological phases of matter. We illustrate this analytically in one of the representative examples, the Su-Schrieffer-Heeger model, finding that spread complexity becomes constant in the topological phase. Moreover, in the same setup, we analyze exactly solvable quench protocols where the evolution of the spread complexity shows distinct dynamical features depending on the topological vs non-topological phase of the initial state as well as the quench Hamiltonian.

Related papers

• Predicting Topological Entanglement Entropy in a Rydberg analog simulator [0.0]
  This work focuses on the dynamical preparation of a quantum-spin-liquid state on a Rydberg-atom simulator. The flexibility of our approach does not only allow one to match the physically correct form of the Rydberg-atom Hamiltonian but also the relevant lattice topology. We show that, while the simulated state exhibits (global) topological order and local properties resembling those of a resonating-valence-bond (RVB) state, it lacks the latter's characteristic topological entanglement entropy signature.
  arXiv  Detail & Related papers  (2024-06-28T12:27:42Z)
• Krylov Complexity and Dynamical Phase Transition in the quenched LMG model [0.0]
  We explore the Krylov complexity in quantum states following a quench in the Lipkin-Meshkov-Glick model. Our results reveal that the long-term averaged Krylov complexity acts as an order parameter for this model. A matching dynamic behavior is observed in both bases when the initial state possesses a specific symmetry.
  arXiv  Detail & Related papers  (2023-12-08T19:11:55Z)
• Softening of Majorana edge states by long-range couplings [77.34726150561087]
  Long-range couplings in the Kitaev chain is shown to modify the universal scaling of topological states close to the critical point. We prove that the Majorana states become increasingly delocalised at a universal rate which is only determined by the interaction range.
  arXiv  Detail & Related papers  (2023-01-29T19:00:08Z)
• Topological transitions of the generalized Pancharatnam-Berry phase [55.41644538483948]
  We show that geometric phases can be induced by a sequence of generalized measurements implemented on a single qubit. We demonstrate and study this transition experimentally employing an optical platform. Our protocol can be interpreted in terms of environment-induced geometric phases.
  arXiv  Detail & Related papers  (2022-11-15T21:31:29Z)
• Spread Complexity and Topological Transitions in the Kitaev Chain [1.4973636284231042]
  We use a 1-dimensional p-wave superconductor as a prototype of a system displaying a topological phase transition. The Hamiltonian of the Kitaev chain manifests two gapped phases of matter with fermion parity symmetry. We show that Krylov-complexity is able to distinguish between the two and provides a diagnostic of the quantum critical point that separates them.
  arXiv  Detail & Related papers  (2022-08-12T14:52:28Z)
• Accessing the topological Mott insulator in cold atom quantum simulators with realistic Rydberg dressing [58.720142291102135]
  We investigate a realistic scenario for the quantum simulation of such systems using cold Rydberg-dressed atoms in optical lattices. We perform a detailed analysis of the phase diagram at half- and incommensurate fillings, in the mean-field approximation. We furthermore study the stability of the phases with respect to temperature within the mean-field approximation.
  arXiv  Detail & Related papers  (2022-03-28T14:55:28Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Characterizing Topological Excitations of a Long-Range Heisenberg Model with Trapped Ions [0.0]
  We propose a Floquet protocol to realize the antiferromagnetic Heisenberg model with power-law decaying interactions. We show that this model features a quantum phase transition from a liquid to a valence bond solid that spontaneously breaks lattice translational symmetry. We moreover introduce an interferometric protocol to characterize the topological excitations and the bulk topological invariants of the interacting many-body system.
  arXiv  Detail & Related papers  (2020-12-16T19:00:02Z)
• Quantum Circuit Complexity of Primordial Perturbations [0.0]
  We study the quantum circuit complexity of cosmological perturbations in different models of the early universe. Our analysis serves to highlight how different models achieve the same end result for the perturbations via different routes.
  arXiv  Detail & Related papers  (2020-12-09T08:30:07Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)
• Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
  We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
  arXiv  Detail & Related papers  (2020-01-16T17:44:52Z)

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.