Kac-Moody symmetries in one-dimensional bosonic systems

• URL: http://arxiv.org/abs/2304.00609v3
• Date: Tue, 1 Aug 2023 10:02:42 GMT
• Title: Kac-Moody symmetries in one-dimensional bosonic systems
• Authors: Wei Tang, Jutho Haegeman
• Abstract summary: In conformal field theories, when the conformal symmetry is enhanced by a global Lie group symmetry, the original Virasoro algebra can be extended to Kac-Moody algebra. We extend the lattice construction of the Kac-Moody generators to continuous systems and apply it to one-dimensional continuous boson systems.
• Score: 19.707384009550843
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In conformal field theories, when the conformal symmetry is enhanced by a global Lie group symmetry, the original Virasoro algebra can be extended to Kac-Moody algebra. In this paper, we extend the lattice construction of the Kac-Moody generators introduced in Wang et al., [Phys. Rev. B. 106, 115111 (2022)] to continuous systems and apply it to one-dimensional continuous boson systems. We justify this microscopic construction of Kac-Moody generators in two ways. First, through phenomenological bosonization, we express the microscopic construction in terms of the boson operators in the bosonization context, which can be related to the Kac-Moody generators in conformal field theories. Second, we study the behavior of the Kac-Moody generators in the integrable Lieb-Liniger model, and reveal its underlying particle-hole excitation picture through Bethe ansatz solutions. Finally, we test the computation of the Kac-Moody generator in the continuous matrix product state simulations, paving the way for more challenging non-integrable systems.

Related papers

• Chiral Virasoro algebra from a single wavefunction [14.735587711294299]
  When the edge is purely chiral, the Hilbert space of low-energy edge excitations can form a representation of a single Virasoro algebra. We propose a method to systematically extract the generators of the Virasoro algebra from a single ground state wavefunction.
  arXiv  Detail & Related papers  (2024-03-27T09:54:21Z)
• Dynamics of a Generalized Dicke Model for Spin-1 Atoms [0.0]
  The Dicke model is a staple of theoretical cavity Quantum Electrodynamics (cavity QED) It demonstrates a rich variety of dynamics such as phase transitions, phase multistability, and chaos. The varied and complex behaviours admitted by the model highlights the need to more rigorously map its dynamics.
  arXiv  Detail & Related papers  (2024-03-04T04:09:35Z)
• Geometric Phase of a Transmon in a Dissipative Quantum Circuit [44.99833362998488]
  We study the geometric phases acquired by a paradigmatic setup: a transmon coupled to a superconductor resonating cavity. In the dissipative model, the non-unitary effects arise from dephasing, relaxation, and decay of the transmon coupled to its environment. Our approach enables a comparison of the geometric phases obtained in these models, leading to a thorough understanding of the corrections introduced by the presence of the environment.
  arXiv  Detail & Related papers  (2024-01-22T16:41:00Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Higher-order topological Peierls insulator in a two-dimensional atom-cavity system [58.720142291102135]
  We show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The pattern opens a non-trivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states. Our work shows how atomic quantum simulators can be harnessed to investigate novel strongly-correlated topological phenomena.
  arXiv  Detail & Related papers  (2023-05-05T10:25:14Z)
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue [68.8204255655161]
  We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime. We present a scheme for the quantum simulation of this gravitational analogue by means of ultra-cold atoms in Raman optical lattices.
  arXiv  Detail & Related papers  (2022-12-02T18:28:23Z)
• Quantum quenches in a pseudo-Hermitian Chern insulator [1.0093662416275693]
  We show the bulk-surface duality of the pseudo-Hermitian phases, then build a concrete relation between the static band topology and quench dynamics. We propose a possible scheme to realize the seemingly challenging model in a bilayer lattice and detect the dynamics with a double-quench protocol.
  arXiv  Detail & Related papers  (2022-09-30T03:20:45Z)
• Emergence of Kac-Moody Symmetry in Critical Quantum Spin Chains [0.0]
  We numerically investigate the emergence of Kac-Moody symmetry at low energies and long distances. We first propose a method to construct lattice operators corresponding to the Kac-Moody generators. We numerically show that, when projected onto low energy states of the quantum spin chain, these operators indeed approximately fulfill the Kac-Moody algebra.
  arXiv  Detail & Related papers  (2022-06-03T16:02:50Z)
• Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness [68.8204255655161]
  We compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models. In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls. We show the geometric phase is robust, exhibiting a vanishing correction under a non-unitary evolution.
  arXiv  Detail & Related papers  (2021-10-27T15:27:54Z)
• Conformal field theory from lattice fermions [77.34726150561087]
  We provide a rigorous lattice approximation of conformal field theories given in terms of lattice fermions in 1+1-dimensions. We show how these results lead to explicit error estimates pertaining to the quantum simulation of conformal field theories.
  arXiv  Detail & Related papers  (2021-07-29T08:54:07Z)
• Self-consistent microscopic derivation of Markovian master equations for open quadratic quantum systems [0.0]
  We provide a rigorous construction of Markovian master equations for a wide class of quantum systems. We show that, for non-degenerate systems under a full secular approximation, the effective Lindblad operators are the normal modes of the system. We also address the particle and energy current flowing through the system in a minimal two-bath scheme and find that they hold the structure of Landauer's formula.
  arXiv  Detail & Related papers  (2021-01-22T19:25:17Z)

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.