Entanglement-enabled symmetry-breaking orders

• URL: http://arxiv.org/abs/2207.08828v2
• Date: Sat, 23 Mar 2024 19:09:44 GMT
• Title: Entanglement-enabled symmetry-breaking orders
• Authors: Cheng-Ju Lin, Liujun Zou,
• Abstract summary: A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any tensor-product state.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description. For concreteness, we present an infinite family of exactly solvable gapped models on one-dimensional lattices with nearest-neighbor interactions, whose ground states exhibit entanglement-enabled symmetry-breaking orders from a discrete symmetry breaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglement-enabled symmetry-breaking orders with spontaneously broken continuous symmetries. Under the unbroken symmetries, some of our examples can be viewed as symmetry-protected topological states that are beyond the conventional classifications.

Related papers

• Robust Symmetry Detection via Riemannian Langevin Dynamics [39.342336146118015]
  We propose a novel symmetry detection method that marries classical symmetry detection techniques with recent advances in generative modeling. Specifically, we apply Langevin dynamics to a symmetry space to enhance robustness against noise. We provide empirical results on a variety of shapes that suggest our method is not only robust to noise, but can also identify both partial and global symmetries.
  arXiv  Detail & Related papers  (2024-09-18T02:28:20Z)
• Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak [4.41737598556146]
  We show that strong symmetry always spontaneously breaks into the corresponding weak symmetry. We conjecture that this relation among strong-to-weak symmetry breaking, gapless modes, and symmetry-charge diffusion is general for continuous symmetries.
  arXiv  Detail & Related papers  (2024-06-27T17:55:36Z)
• Non-invertible SPT, gauging and symmetry fractionalization [2.541410020898643]
  We construct the lattice models for the phases of all the symmetries in the Rep($Q_8$) duality web. We show that these interplay can be explained using the symmetry fractionalization in the 2+1d bulk SET.
  arXiv  Detail & Related papers  (2024-05-24T21:35:55Z)
• 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)
• Asymmetry activation and its relation to coherence under permutation operation [53.64687146666141]
  A Dicke state and its decohered state are invariant for permutation. When another qubits state to each of them is attached, the whole state is not invariant for permutation, and has a certain asymmetry for permutation.
  arXiv  Detail & Related papers  (2023-11-17T03:33:40Z)
• A universal formula for the entanglement asymmetry of matrix product states [0.0]
  We provide a universal formula for the entanglement asymmetry of matrix product states with finite bond dimension. We show that the entanglement asymmetry of any compact -- discrete or continuous -- group depends only on the symmetry breaking pattern, and is not related to any other microscopic features.
  arXiv  Detail & Related papers  (2023-10-03T11:15:19Z)
• 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)
• Identifying the Group-Theoretic Structure of Machine-Learned Symmetries [41.56233403862961]
  We propose methods for examining and identifying the group-theoretic structure of such machine-learned symmetries. As an application to particle physics, we demonstrate the identification of the residual symmetries after the spontaneous breaking of non-Abelian gauge symmetries.
  arXiv  Detail & Related papers  (2023-09-14T17:03:50Z)
• Machine-learning hidden symmetries [0.0]
  We present an automated method for finding hidden symmetries, defined as symmetries that become manifest only in a new coordinate system that must be discovered. Its core idea is to quantify asymmetry as violation of certain partial differential equations, and to numerically minimize such violation over the space of all invertible transformations, parametrized as invertible neural networks.
  arXiv  Detail & Related papers  (2021-09-20T17:55:02Z)
• Symmetry Breaking in Symmetric Tensor Decomposition [44.181747424363245]
  We consider the nonsymmetry problem associated with computing the points rank decomposition of symmetric tensors. We show that critical points the loss function is detected by standard methods.
  arXiv  Detail & Related papers  (2021-03-10T18:11:22Z)
• 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)

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.