The symmetry of the Hamiltonian describing the asymmetric twin model was partially studied in earlier works, and our aim here is to generalize these results for the open transfer matrix.In this spirit we first prove, that the so called boundary quantum algebra provides a symmetry for any generic -independent of the choice of model -open transfer matrix with a trivial left boundary.In addition it is shown that the boundary quantum algebra is the centralizer of the B type Hecke algebra.We then focus on the asymmetric twin representation of the boundary Temperley-Lieb algebra.More precisely, by exploiting exchange relations dictated by the reflection equation we show that the transfer matrix with trivial boundary conditions enjoys the recognized U q (sl 2 ) ⊗ U i (sl 2 ) symmetry.When a nondiagonal boundary is implemented the symmetry as expected is reduced, however again certain familiar boundary non-local charges turn out to commute with the corresponding transfer matrix.The symmetry of the Hamiltonian describing the asymmetric twin model was partially studied in earlier works, and our aim here is to generalize these results for the open transfer matrix.In this spirit we first prove, that the so called boundary quantum algebra provides a symmetry for any generic -independent of the choice of model -open transfer matrix with a trivial left boundary.In addition it is shown that the boundary quantum algebra is the centralizer of the B type Hecke algebra.We then focus on the asymmetric twin representation of the boundary Temperley-Lieb algebra.More precisely, by exploiting exchange relations dictated by the reflection equation we show that the transfer matrix with trivial boundary conditions enjoys the recognized U q (sl 2 ) ⊗ U i (sl 2 ) symmetry.When a nondiagonal boundary is implemented the symmetry as expected is reduced, however again certain familiar boundary non-local charges turn out to commute with the corresponding transfer matrix.

arXiv:math-ph/0606040Symmetry Integrability and Geometry Methods and ApplicationsJan 9, 20074 citations

QUANTUM NETWORK MODELS AND THEIR SYMMETRY PROPERTIES

Tomi Ohtsuki, Keith Slevin

International Symposium on Topological Aspects of Critical Systems and NetworksJun 1, 20071 citation

Symmetries of quantum systems

Theoretical and mathematical physicsSep 22, 20080 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

Symmetry and quantum systems

Anthony Brinton Wolbarst

Jan 1, 19776 citations

Large N matrix quantum mechanics as a quantum memory

ChunJun Cao, Gong Cheng, Brian G. Swingle

In this paper, we explore the possibility of building a quantum memory that is robust to thermal noise using large $N$ matrix quantum mechanics models. First, we investigate the gauged $SU(N)$ matrix harmonic oscillator and different ways to encode quantum information in it. By calculating the mutual information between the system and a reference which purifies the encoded information, we identify a transition temperature, ${T}_{c}$ , below which the encoded quantum information is protected from thermal noise for a memory time scaling as ${N}^{2}$ . Conversely, for temperatures higher than ${T}_{c}$ , the information is quickly destroyed by thermal noise. Second, we relax the requirement of gauge invariance and study a matrix harmonic oscillator model with only global symmetry. Finally, we further relax even the symmetry requirement and propose a model that consists of a large number ${N}^{2}$ of qubits, with interactions derived from an approximate $SU(N)$ symmetry. In both ungauged models, we find that the effects of gauging can be mimicked using an energy penalty to give a similar result for the memory time. The final qubit model also has the potential to be realized in the laboratory.In this paper, we explore the possibility of building a quantum memory that is robust to thermal noise using large $N$ matrix quantum mechanics models. First, we investigate the gauged $SU(N)$ matrix harmonic oscillator and different ways to encode quantum information in it. By calculating the mutual information between the system and a reference which purifies the encoded information, we identify a transition temperature, ${T}_{c}$, below which the encoded quantum information is protected from thermal noise for a memory time scaling as ${N}^{2}$. Conversely, for temperatures higher than ${T}_{c}$, the information is quickly destroyed by thermal noise. Second, we relax the requirement of gauge invariance and study a matrix harmonic oscillator model with only global symmetry. Finally, we further relax even the symmetry requirement and propose a model that consists of a large number ${N}^{2}$ of qubits, with interactions derived from an approximate $SU(N)$ symmetry. In both ungauged models, we find that the effects of gauging can be mimicked using an energy penalty to give a similar result for the memory time. The final qubit model also has the potential to be realized in the laboratory.

Physical review. D/Physical review. D.Oct 10, 20232 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 this paper, we explore the possibility of building a quantum memory that is robust to thermal noise using large

N

matrix quantum mechanics models. First, we investigate the gauged

SU(N)

matrix harmonic oscillator and different ways to encode quantum information in it. By calculating the mutual information between the system and a reference which purifies the encoded information, we identify a transition temperature,

{T}_{c}

, below which the encoded quantum information is protected from thermal noise for a memory time scaling as

{N}^{2}

. Conversely, for temperatures higher than

{T}_{c}

, the information is quickly destroyed by thermal noise. Second, we relax the requirement of gauge invariance and study a matrix harmonic oscillator model with only global symmetry. Finally, we further relax even the symmetry requirement and propose a model that consists of a large number

{N}^{2}

of qubits, with interactions derived from an approximate

SU(N)

symmetry. In both ungauged models, we find that the effects of gauging can be mimicked using an energy penalty to give a similar result for the memory time. The final qubit model also has the potential to be realized in the laboratory.