Abstract Symmetry breaking is a fundamental concept in understanding quantum phases of matter, studied so far mostly through the lens of local order parameters. Recently, a new entanglement-based probe of symmetry breaking has been introduced under the name of entanglement asymmetry , which has been employed to investigate the mechanism of dynamical symmetry restoration. Here, we provide a universal formula for the entanglement asymmetry of matrix product states with finite bond dimension, valid in the large volume limit. 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.Abstract Symmetry breaking is a fundamental concept in understanding quantum phases of matter, studied so far mostly through the lens of local order parameters. Recently, a new entanglement-based probe of symmetry breaking has been introduced under the name of entanglement asymmetry , which has been employed to investigate the mechanism of dynamical symmetry restoration. Here, we provide a universal formula for the entanglement asymmetry of matrix product states with finite bond dimension, valid in the large volume limit. 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:2310.01962Journal of Physics A Mathematical and TheoreticalOct 16, 202437 citations

Diagonalization with matrix-product states

Chen Liu, Anders W. Sandvik

Bulletin of the American Physical SocietyMar 23, 20110 citations

Matrix product states with adaptive global symmetries

Chu Guo, Dario Poletti

Quantum many-body physics simulations with matrix product states can often be accelerated if the quantum symmetries present in the system are explicitly taken into account. Conventionally, quantum symmetries have to be determined beforehand when constructing the tensors for the matrix product state algorithm. In this work, we present a matrix product state algorithm with an adaptive $U(1)$ symmetry. This algorithm can take into account or benefit from $U(1)$ or ${Z}_{2}$ symmetries when they are present or analyze the nonsymmetric scenario when the symmetries are broken without any external alteration of the code. To give some concrete examples we consider an XYZ model and show the insight that can be gained by (i) searching the ground state and (ii) evolving in time after a symmetry-changing quench. To show the generality of the method, we also consider an interacting bosonic system under the effect of a symmetry-breaking dissipation.Quantum many-body physics simulations with matrix product states can often be accelerated if the quantum symmetries present in the system are explicitly taken into account. Conventionally, quantum symmetries have to be determined beforehand when constructing the tensors for the matrix product state algorithm. In this work, we present a matrix product state algorithm with an adaptive $U(1)$ symmetry. This algorithm can take into account or benefit from $U(1)$ or ${Z}_{2}$ symmetries when they are present or analyze the nonsymmetric scenario when the symmetries are broken without any external alteration of the code. To give some concrete examples we consider an XYZ model and show the insight that can be gained by (i) searching the ground state and (ii) evolving in time after a symmetry-changing quench. To show the generality of the method, we also consider an interacting bosonic system under the effect of a symmetry-breaking dissipation.

arXiv:1905.01609Physical review. B./Physical review. BOct 14, 20196 citations

Classifying parafermionic gapped phases using matrix product states

Wen-Tao Xu, Guang-Ming Zhang

In the Fock representation, we construct matrix product states (MPS) for one-dimensional gapped phases for ${\mathbb{Z}}_{p}$ parafermions. From the analysis of irreducibility of MPS, we classify all possible gapped phases of ${\mathbb{Z}}_{p}$ parafermions without extra symmetry other than ${\mathbb{Z}}_{p}$ charge symmetry, including topological phases, spontaneous symmetry breaking phases, and a trivial phase. For all phases, we find the irreducible forms of local matrices of MPS, which span different kinds of graded algebras. The topological phases are characterized by the nontrivial simple ${\mathbb{Z}}_{p}$ graded algebras with the characteristic graded centers, yielding the degeneracies of the full transfer matrix spectra uniquely. However, the spontaneous symmetry breaking phases correspond to the trivial semisimple ${\mathbb{Z}}_{p/n}$ graded algebras, which can be further reduced to the trivial simple ${\mathbb{Z}}_{p/n}$ graded algebras, where $n$ is the divisor of $p$ . So the present results provide the complete classification of the parafermionic gapped phases and deepen our understanding of topological phases in one dimension.In the Fock representation, we construct matrix product states (MPS) for one-dimensional gapped phases for ${\mathbb{Z}}_{p}$ parafermions. From the analysis of irreducibility of MPS, we classify all possible gapped phases of ${\mathbb{Z}}_{p}$ parafermions without extra symmetry other than ${\mathbb{Z}}_{p}$ charge symmetry, including topological phases, spontaneous symmetry breaking phases, and a trivial phase. For all phases, we find the irreducible forms of local matrices of MPS, which span different kinds of graded algebras. The topological phases are characterized by the nontrivial simple ${\mathbb{Z}}_{p}$ graded algebras with the characteristic graded centers, yielding the degeneracies of the full transfer matrix spectra uniquely. However, the spontaneous symmetry breaking phases correspond to the trivial semisimple ${\mathbb{Z}}_{p/n}$ graded algebras, which can be further reduced to the trivial simple ${\mathbb{Z}}_{p/n}$ graded algebras, where $n$ is the divisor of $p$. So the present results provide the complete classification of the parafermionic gapped phases and deepen our understanding of topological phases in one dimension.

arXiv:1705.01745Physical review. B./Physical review. BJan 30, 20184 citations

QUANTUM MECHANICAL SYMMETRY BREAKING

R. Jackiw

Elsevier eBooksJan 1, 19852 citations

U(1)

symmetry. This algorithm can take into account or benefit from

U(1)

{Z}_{2}

symmetries when they are present or analyze the nonsymmetric scenario when the symmetries are broken without any external alteration of the code. To give some concrete examples we consider an XYZ model and show the insight that can be gained by (i) searching the ground state and (ii) evolving in time after a symmetry-changing quench. To show the generality of the method, we also consider an interacting bosonic system under the effect of a symmetry-breaking dissipation.

In the Fock representation, we construct matrix product states (MPS) for one-dimensional gapped phases for

{\mathbb{Z}}_{p}

parafermions. From the analysis of irreducibility of MPS, we classify all possible gapped phases of

{\mathbb{Z}}_{p}

parafermions without extra symmetry other than

{\mathbb{Z}}_{p}

charge symmetry, including topological phases, spontaneous symmetry breaking phases, and a trivial phase. For all phases, we find the irreducible forms of local matrices of MPS, which span different kinds of graded algebras. The topological phases are characterized by the nontrivial simple

{\mathbb{Z}}_{p}

graded algebras with the characteristic graded centers, yielding the degeneracies of the full transfer matrix spectra uniquely. However, the spontaneous symmetry breaking phases correspond to the trivial semisimple

{\mathbb{Z}}_{p/n}

graded algebras, which can be further reduced to the trivial simple

{\mathbb{Z}}_{p/n}

graded algebras, where

n

is the divisor of

p

. So the present results provide the complete classification of the parafermionic gapped phases and deepen our understanding of topological phases in one dimension.