Higher structures in matrix product states

• URL: http://arxiv.org/abs/2304.05356v2
• Date: Sat, 15 Apr 2023 13:30:22 GMT
• Title: Higher structures in matrix product states
• Authors: Shuhei Ohyama, Shinsei Ryu
• Abstract summary: We introduce a gerbe structure, a higher generalization of complex line bundles, as an underlying mathematical structure describing topological properties of a parameterized family of matrix product states. We also introduce a "triple inner product" for three matrix product states, which allows us to extract a topological invariant, the Dixmier-Douady class over the parameter space.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: For a parameterized family of invertible states (short-range-entangled states) in $(1+1)$ dimensions, we discuss a generalization of the Berry phase. Using translationally-invariant, infinite matrix product states (MPSs), we introduce a gerbe structure, a higher generalization of complex line bundles, as an underlying mathematical structure describing topological properties of a parameterized family of matrix product states. We also introduce a "triple inner product" for three matrix product states, which allows us to extract a topological invariant, the Dixmier-Douady class over the parameter space.

Related papers

• Matrix Ordering through Spectral and Nilpotent Structures in Totally Ordered Complex Number Fields [2.2533084621250143]
  We develop a total ordering relation for complex numbers, enabling comparisons of the spectral components of general matrices with complex eigenvalues. We establish a theoretical framework for majorization ordering with complex-valued functions. We characterize Jordan blocks of matrix functions using a generalized dominance order for nilpotent components.
  arXiv  Detail & Related papers  (2025-01-17T23:34:17Z)
• Topological nature of edge states for one-dimensional systems without symmetry protection [46.87902365052209]
  We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbour (between unit cells) Our invariant is invariant under unitary and similarity transforms.
  arXiv  Detail & Related papers  (2024-12-13T19:44:54Z)
• Efficient conversion from fermionic Gaussian states to matrix product states [48.225436651971805]
  We propose a highly efficient algorithm that converts fermionic Gaussian states to matrix product states. It can be formulated for finite-size systems without translation invariance, but becomes particularly appealing when applied to infinite systems. The potential of our method is demonstrated by numerical calculations in two chiral spin liquids.
  arXiv  Detail & Related papers  (2024-08-02T10:15:26Z)
• Higher Berry Connection for Matrix Product States [0.0]
  We introduce a connection, the higher Berry connection, for a family of parameterized Matrix Product States (MPS) over a parameter space. We demonstrate the use of our formula for simple non-trivial models.
  arXiv  Detail & Related papers  (2024-05-08T18:00:33Z)
• Higher Berry Phase from Projected Entangled Pair States in (2+1) dimensions [0.0]
  We consider families of invertible many-body quantum states in $d$ spatial dimensions that are parameterized over some parameter space $X$. The space of such families is expected to have topologically distinct sectors classified by the cohomology group $mathrmHd+2(X;mathbbZ)$.
  arXiv  Detail & Related papers  (2024-05-08T18:00:20Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• 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)
• $h(1) \oplus su(2)$ vector algebra eigenstates with eigenvalues in the matrix domain [0.0]
  We find a subset of generalized vector coherent states in the matrix domain. For a special choice of the matrix eigenvalue parameters we found the so-called vector coherent states with matrices associated to the Heisenberg-Weyl group.
  arXiv  Detail & Related papers  (2023-01-25T18:10:01Z)
• Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation [64.49871502193477]
  We propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. Comprehensive experimental results on six commonly-used benchmark datasets demonstrate the superiority of our method over state-of-the-art methods.
  arXiv  Detail & Related papers  (2022-05-21T01:47:17Z)
• Non-Markovian Stochastic Schr\"odinger Equation: Matrix Product State Approach to the Hierarchy of Pure States [65.25197248984445]
  We derive a hierarchy of matrix product states (HOMPS) for non-Markovian dynamics in open finite temperature. The validity and efficiency of HOMPS is demonstrated for the spin-boson model and long chains where each site is coupled to a structured, strongly non-Markovian environment.
  arXiv  Detail & Related papers  (2021-09-14T01:47:30Z)
• Diagonal unitary and orthogonal symmetries in quantum theory [1.5229257192293197]
  We show that this class of matrices (and maps) encompasses a wide variety of scenarios, thereby unifying their study. For linear maps, we provide explicit characterizations of the stated covariance in terms of their Kraus, Stinespring, and Choi representations. We also describe the invariant subspaces of these maps and use their structure to provide necessary and sufficient conditions for separability of the associated invariant bipartite states.
  arXiv  Detail & Related papers  (2020-10-15T17:25:38Z)

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.