Disorder-free localisation in continuous-time quantum walks : Role of symmetries
arXiv:2307.01963 · doi:10.1103/PhysRevA.109.012205
Abstract
We investigate the phenomenon of disorder-free localisation in quantum systems with global permutation symmetry. We use permutation group theory to systematically construct permutation symmetric many-fermion Hamiltonians and interpret them as generators of continuous-time quantum walks. When the number of fermions is very large we find that all the canonical basis states localise at all times, without the introduction of any disorder coefficients. This time-independent localisation is not the result of any emergent disorder distinguishing it from existing mechanisms for disorder-free localisation. Next we establish the conditions under which the localisation is preserved. We find that interactions that preserve and break the global permutation symmetry sustains localisation. Furthermore the basis states of systems with reduced permutation symmetry, localise even for a small number of fermions when the symmetry-reducing parameters are tuned accordingly. We show that similar localisation also occurs for a permutation symmetric Heisenberg spin chain and permutation symmetric bosonic systems, implying that the localisation is independent of the superselected symmetry. Finally we make connections of the Hamiltonians studied here to the adjacency matrices of graphs and use this to propose a prescription for disorder-free localisation in continuous-time quantum walk systems. Many of the models proposed here feature all-to-all connectivity and can be potentially realised on superconducting quantum circuits, trapped ion systems and ultracold atoms.
v3 - 45 pages, 5 figures, published version, includes stability analysis, Author list in alphabetical order
References in corpus (28)
- Universal computation by quantum walk
- Universal computation by multi-particle quantum walk
- Ultracold Fermi Gases with Emergent SU(N) Symmetry
- Many-body localization dynamics from gauge invariance
- Loschmidt Echo
- Quantum Simulations of Classical Annealing Processes
- Entanglement and Particle Identity: A Unifying Approach
- Entanglement, Particle Identity and the GNS Construction: A Unifying Approach
- Entanglement in indistinguishable particle systems
- Symmetries and noise in quantum walk
- Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions
- Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems
- Quantum walk approach to simulating parton showers
- Fully-connected network of superconducting qubits in a cavity
- Exact analytical results for quantum walks on star graph
- Long-range connectivity in a superconducting quantum processor using a ring resonator
- Two bosonic quantum walkers in one-dimensional optical lattices
- Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium
- On the Spectral Form Factor for Random Matrices
- Disorder-free localization with Stark gauge protection
- Disorder-free localization in quantum walks
- Swift chiral quantum walks
- Non-thermal dynamics in a spin-1/2 lattice Schwinger model
- Two-level Quantum Walkers on Directed Graphs I: Universal Quantum Computing
- Stable interaction-induced Anderson-like localization embedded in standing waves
- Interacting Stark localization dynamics in a three-dimensional lattice Bose gas
- Local subgraph structure can cause localization in continuous-time quantum walk
- Localization of two-dimensional quantum walks defined by generalized Grover coins