Categorical Symmetries in Spin Models with Atom Arrays

• URL: http://arxiv.org/abs/2412.15024v2
• Date: Wed, 19 Feb 2025 15:06:51 GMT
• Title: Categorical Symmetries in Spin Models with Atom Arrays
• Authors: Alison Warman, Fan Yang, Apoorv Tiwari, Hannes Pichler, Sakura Schafer-Nameki,
• Abstract summary: Categorical symmetries have recently been shown to generalize the classification of phases of matter. We propose a simple spin chain model that encompasses all gapped phases and second-order phase transitions.
• Score: 2.321156230142032
• License:
• Abstract: Categorical symmetries have recently been shown to generalize the classification of phases of matter, significantly broadening the traditional Landau paradigm. To test these predictions, we propose a simple spin chain model that encompasses all gapped phases and second-order phase transitions governed by the categorical symmetry $\mathsf{Rep}(D_8)$. This model not only captures the essential features of non-invertible phases but is also straightforward enough to enable practical realization. Specifically, we outline an implementation using neutral atoms trapped in optical tweezer arrays. Employing a dual-species setup and Rydberg blockade, we propose a digital simulation approach that can efficiently implement the many-body evolution in several nontrivial quantum phases.

Related papers

• Distinguishing Ordered Phases using Machine Learning and Classical Shadows [0.3769303106863453]
  This work proposes a framework for identifying quantum phase transitions by combining classical shadows with unsupervised machine learning. Even with few qubits, we can effectively distinguish between the different phases of the Hamiltonian models.
  arXiv  Detail & Related papers  (2025-01-29T18:35:40Z)
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling [0.0]
  Quantum circuits offer a versatile platform for simulating digital quantum dynamics. We show that monitored quantum circuits yield robust phases of dynamic matter. Our work further solidifies the concept of emergent circuit phases and their phase transitions.
  arXiv  Detail & Related papers  (2024-09-03T18:00:01Z)
• Entanglement and the density matrix renormalisation group in the generalised Landau paradigm [0.0]
  We leverage the interplay between gapped phases and dualities of symmetric one-dimensional quantum lattice models. For every phase in the phase diagram, the dual representation of the ground state that breaks all symmetries minimises both the entanglement entropy and the required number of variational parameters. Our work testifies to the usefulness of generalised non-invertible symmetries and their formal category theoretic description for the nuts and bolts simulation of strongly correlated systems.
  arXiv  Detail & Related papers  (2024-08-12T17:51:00Z)
• On the Emergence of Cross-Task Linearity in the Pretraining-Finetuning Paradigm [47.55215041326702]
  We discover an intriguing linear phenomenon in models that are from a common pretrained checkpoint and finetuned on different tasks, termed as Cross-Task Linearity (CTL) We show that if we linearly interpolate the weights of two finetuned models, the features in the weight-interpolated model are often approximately equal to the linearities of features in two finetuned models at each layer. We conjecture that in the pretraining-finetuning paradigm, neural networks approximately function as linear maps, mapping from the parameter space to the feature space.
  arXiv  Detail & Related papers  (2024-02-06T03:28:36Z)
• Exotic Symmetry Breaking Properties of Self-Dual Fracton Spin Models [4.467896011825295]
  We investigate the ground-state properties and phase transitions of two self-dual fracton spin models. We show that both models experience a strong first-order phase transition with an anomalous $L-(D-1)$ scaling. Our work provides new understanding of sub-dimensional symmetry breaking and makes an important step for studying quantum-error-correction properties of the checkerboard and Haah's codes.
  arXiv  Detail & Related papers  (2023-11-18T13:12:14Z)
• Theory of mobility edge and non-ergodic extended phase in coupled random matrices [18.60614534900842]
  The mobility edge, as a central concept in disordered models for localization-delocalization transitions, has rarely been discussed in the context of random matrix theory. We show that their overlapped spectra and un-overlapped spectra exhibit totally different scaling behaviors, which can be used to construct tunable mobility edges. Our model provides a general framework to realize the mobility edges and non-ergodic phases in a controllable way in RMT.
  arXiv  Detail & Related papers  (2023-11-15T01:43:37Z)
• Oracle-Preserving Latent Flows [58.720142291102135]
  We develop a methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to transformations invariant with respect to high-dimensional oracles.
  arXiv  Detail & Related papers  (2023-02-02T00:13:32Z)
• Spin-spin coupling-based quantum and classical phase transitions in two-impurity spin-boson models [55.41644538483948]
  Two-interacting-impurity spin-boson models with vanishing transverse fields on the spin-pair are studied. The dynamics of the magnetization is analysed for different levels of (an)isotropy.
  arXiv  Detail & Related papers  (2022-05-19T08:01:03Z)
• Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice [52.77024349608834]
  We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and non-local terms gives rise to a phase diagram with liquid phases with dominant cluster, spin, and density-wave quasi-long-range ordering.
  arXiv  Detail & Related papers  (2021-12-20T09:46:08Z)
• Probing the topological Anderson transition with quantum walks [48.7576911714538]
  We consider one-dimensional quantum walks in optical linear networks with synthetically introduced disorder and tunable system parameters. The option to directly monitor the walker's probability distribution makes this optical platform ideally suited for the experimental observation of the unique signatures of the one-dimensional topological Anderson transition.
  arXiv  Detail & Related papers  (2021-02-01T21:19:15Z)
• Kernel and Rich Regimes in Overparametrized Models [69.40899443842443]
  We show that gradient descent on overparametrized multilayer networks can induce rich implicit biases that are not RKHS norms. We also demonstrate this transition empirically for more complex matrix factorization models and multilayer non-linear networks.
  arXiv  Detail & Related papers  (2020-02-20T15:43:02Z)

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.