Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications

• URL: http://arxiv.org/abs/2309.15167v3
• Date: Fri, 29 Nov 2024 19:00:02 GMT
• Title: Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Authors: Sanjay Moudgalya, Olexei I. Motrunich,
• Abstract summary: We show that symmetry algebras of quantum many-body systems with locality can be expressed as frustration-free ground states of a local superoperator. In addition, we show that the low-energy excitations of this super-Hamiltonian can be understood as approximate symmetries.
• Score: 0.0
• License:
• Abstract: Symmetry algebras of quantum many-body systems with locality can be understood using commutant algebras, which are defined as algebras of operators that commute with a given set of local operators. In this work, we show that these symmetry algebras can be expressed as frustration-free ground states of a local superoperator, which we refer to as a ``super-Hamiltonian". We demonstrate this for conventional symmetries such as $Z_2$, $U(1)$, and $SU(2)$, where the symmetry algebras map to various kinds of ferromagnetic ground states, as well as for unconventional ones that lead to weak ergodicity breaking phenomena of Hilbert space fragmentation and quantum many-body scars. In addition, we show that the low-energy excitations of this super-Hamiltonian can be understood as approximate symmetries, which in turn are related to slowly relaxing hydrodynamic modes in symmetric systems. This connection is made precise by relating the super-Hamiltonian to the superoperator that governs the operator relaxation in noisy symmetric Brownian circuits, and this physical interpretation also provides a novel interpretation for Mazur bounds for autocorrelation functions. We find examples of gapped/gapless super-Hamiltonians indicating the absence/presence of slow-modes, which happens in the presence of discrete/continuous symmetries. In the gapless cases, we recover hydrodynamic modes such as diffusion, tracer diffusion, and asymptotic scars in the presence of $U(1)$ symmetry, Hilbert space fragmentation, and a tower of quantum scars respectively. In all, this demonstrates the power of the commutant algebra framework in obtaining a comprehensive understanding of exact symmetries, and associated approximate symmetries and hydrodynamic modes, and their dynamical consequences in systems with locality.

Related papers

• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• Latent Space Symmetry Discovery [31.28537696897416]
  We propose a novel generative model, Latent LieGAN, which can discover symmetries of nonlinear group actions. We show that our model can express nonlinear symmetries under some conditions about the group action. LaLiGAN also results in a well-structured latent space that is useful for downstream tasks including equation discovery and long-term forecasting.
  arXiv  Detail & Related papers  (2023-09-29T19:33:01Z)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• Dynamical symmetry algebra of two superintegrable two-dimensional systems [0.0]
  We will re-examine two pseudo-Hermitian quantum systems $E_8$ and $E_10$ from such a classification. Those extra ladder operators are exploited to obtain the generating spectrum algebra and the dynamical symmetry one.
  arXiv  Detail & Related papers  (2022-03-12T14:24:56Z)
• Approximately Equivariant Networks for Imperfectly Symmetric Dynamics [24.363954435050264]
  We find that our models can outperform both baselines with no symmetry bias and baselines with overly strict symmetry in both simulated turbulence domains and real-world multi-stream jet flow.
  arXiv  Detail & Related papers  (2022-01-28T07:31:28Z)
• Symmetry protected entanglement in random mixed states [0.0]
  We study the effect of symmetry on tripartite entanglement properties of typical states in symmetric sectors of Hilbert space. In particular, we consider Abelian symmetries and derive an explicit expression for the logarithmic entanglement negativity of systems with $mathbbZ_N$ and $U(1)$ symmetry groups.
  arXiv  Detail & Related papers  (2021-11-30T19:00:07Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Latent symmetry induced degeneracies [0.0]
  We develop an approach to explain degeneracies by tracing them back to symmetries of an isospectral effective Hamiltonian. As an application, we relate the degeneracies induced by the rotation symmetry of a real Hamiltonian to a non-abelian latent symmetry group.
  arXiv  Detail & Related papers  (2020-11-26T17:37:30Z)
• Quantum jump Monte Carlo simplified: Abelian symmetries [0.0]
  We show how to encode the weak symmetry in quantum dynamics of a finitely dimensional open quantum system. Our results generalize directly to the case of multiple Abelian weak symmetries.
  arXiv  Detail & Related papers  (2020-10-16T16:48:58Z)
• Group Theoretical Approach to Pseudo-Hermitian Quantum Mechanics with Lorentz Covariance and $c \rightarrow \infty $ Limit [0.0]
  The basic representation is identified as a coherent state representation, essentially an irreducible component of the regular representation. The key feature of the formulation is that it is not unitary but pseudo-unitary, exactly in the same sense as the Minkowski spacetime representation. Explicit wavefunction description is given without any restriction of the variable domains, yet with a finite integral inner product.
  arXiv  Detail & Related papers  (2020-09-12T23:48:52Z)
• 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)

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.