Symmetry-Protected Topological relationship between $SU(3)$ and $SU(2)\times{U(1)}$ in Two DimensionSymmetry-Protected Topological relationship between $SU(3)$ and $SU(2)\times{U(1)}$ in Two Dimension

Ning Wang, Qiao Zhuang

Symmetry-protected topological $\left(SPT\right)$ phases are gapped short-range entangled states with symmetry $G$ , which can be systematically described by group cohomology theory. $SU(3)$ and $SU(2)\times{U(1)}$ are considered as the basic groups of Quantum Chromodynamics and Weak-Electromagnetic unification, respectively. In two dimension $(2D)$ , nonlinear-sigma models with a quantized topological Theta term can be used to describe nontrivial SPT phases. By coupling the system to a probe field and integrating out the group variables, the Theta term becomes the effective action of Chern-Simons theory which can derive the response current density. As a result, the current shows a spin Hall effect, and the quantized number of the spin Hall conductance of SPT phases $SU(3)$ and $SU(2)\times{U(1)}$ are same. In addition, relationships between $SU(3)$ and $SU(2)\times{U(1)}$ which maps $SU(3)$ to $SU(2)$ with a rotation $U(1)$ will be given.Symmetry-protected topological $\left(SPT\right)$ phases are gapped short-range entangled states with symmetry $G$, which can be systematically described by group cohomology theory. $SU(3)$ and $SU(2)\times{U(1)}$ are considered as the basic groups of Quantum Chromodynamics and Weak-Electromagnetic unification, respectively. In two dimension $(2D)$, nonlinear-sigma models with a quantized topological Theta term can be used to describe nontrivial SPT phases. By coupling the system to a probe field and integrating out the group variables, the Theta term becomes the effective action of Chern-Simons theory which can derive the response current density. As a result, the current shows a spin Hall effect, and the quantized number of the spin Hall conductance of SPT phases $SU(3)$ and $SU(2)\times{U(1)}$ are same. In addition, relationships between $SU(3)$ and $SU(2)\times{U(1)}$ which maps $SU(3)$ to $SU(2)$ with a rotation $U(1)$ will be given.

arXiv:2101.03359Jan 9, 20210 citations

Vortices in the Su(n) X Su(n) Spin Systems in Two Dimensions.

Robert J. Kares

Jan 1, 19820 citations

Simulation of the dynamics of many-body quantum spin systems using phase-space techniques

Ray Jia Hong Ng, Erik Schwartz Sørensen, Piotr Deuar

We reformulate the full quantum dynamics of spin systems using a phase-space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations. This representation is superior in practice to an earlier phase-space approach based on Schwinger bosons, with the numerical effort scaling only linearly with system size. By also implementing extrapolation techniques from quasiclassical equations to the full quantum limit, we are able to extend useful simulation times severalfold. This approach is applicable in any dimension including cases where frustration is present in the spin system. The method is demonstrated by simulating quenches in the transverse-field Ising model in one and two dimensions.We reformulate the full quantum dynamics of spin systems using a phase-space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations. This representation is superior in practice to an earlier phase-space approach based on Schwinger bosons, with the numerical effort scaling only linearly with system size. By also implementing extrapolation techniques from quasiclassical equations to the full quantum limit, we are able to extend useful simulation times severalfold. This approach is applicable in any dimension including cases where frustration is present in the spin system. The method is demonstrated by simulating quenches in the transverse-field Ising model in one and two dimensions.

arXiv:1307.3786Physical Review BOct 4, 201318 citations

Phase transition of S=12 two-leg Heisenberg spin ladder systems with a four-spin interaction

Keigo Hijii, K. Nomura

We study a phase transition and critical properties of the quantum spin ladder system with a four-spin interaction. We determine a phase boundary between a rung singlet and a staggered dimer phases numerically. This phase transition is of a second order in the weak-coupling region. We confirm that this universality class is described by the $k=2$ SU(2) Wess-Zumino-Witten model, analyzing the central charge and scaling dimensions. In the strong-coupling region, phase transition becomes of a first order.We study a phase transition and critical properties of the quantum spin ladder system with a four-spin interaction. We determine a phase boundary between a rung singlet and a staggered dimer phases numerically. This phase transition is of a second order in the weak-coupling region. We confirm that this universality class is described by the $k=2$ SU(2) Wess-Zumino-Witten model, analyzing the central charge and scaling dimensions. In the strong-coupling region, phase transition becomes of a first order.

Physical Review BJul 23, 20099 citations

On the phase transitions in quantum spin systems

R. Micnas, K. A. Chao

Physics Letters AJul 1, 19853 citations

Symmetry-Protected Topological relationship between

SU(3)

and

SU(2)\times{U(1)}

in Two Dimension

Symmetry-protected topological

\left(SPT\right)

phases are gapped short-range entangled states with symmetry

G

, which can be systematically described by group cohomology theory.

SU(3)

and

SU(2)\times{U(1)}

are considered as the basic groups of Quantum Chromodynamics and Weak-Electromagnetic unification, respectively. In two dimension

(2D)

, nonlinear-sigma models with a quantized topological Theta term can be used to describe nontrivial SPT phases. By coupling the system to a probe field and integrating out the group variables, the Theta term becomes the effective action of Chern-Simons theory which can derive the response current density. As a result, the current shows a spin Hall effect, and the quantized number of the spin Hall conductance of SPT phases

SU(3)

and

SU(2)\times{U(1)}

are same. In addition, relationships between

SU(3)

and

SU(2)\times{U(1)}

which maps

SU(3)

SU(2)

with a rotation

U(1)

will be given.

k=2

SU(2) Wess-Zumino-Witten model, analyzing the central charge and scaling dimensions. In the strong-coupling region, phase transition becomes of a first order.