Quantum spin systems with strong geometric restrictions give rise to rich quantum phases such as valence bond solids and spin liquid states. However, the geometric restrictions often hamper the application of sophisticated numerical approaches. Based on the stochastic series expansion method, we develop an efficient and exact quantum Monte Carlo ``sweeping cluster'' algorithm which automatically satisfies the geometrical restrictions. Here we use the quantum dimer model as a benchmark to demonstrate the reliability and power of this algorithm. Comparing to existing numerical methods, we can obtain higher accuracy results for a wider parameter region and much more substantial system sizes.Quantum spin systems with strong geometric restrictions give rise to rich quantum phases such as valence bond solids and spin liquid states. However, the geometric restrictions often hamper the application of sophisticated numerical approaches. Based on the stochastic series expansion method, we develop an efficient and exact quantum Monte Carlo ``sweeping cluster'' algorithm which automatically satisfies the geometrical restrictions. Here we use the quantum dimer model as a benchmark to demonstrate the reliability and power of this algorithm. Comparing to existing numerical methods, we can obtain higher accuracy results for a wider parameter region and much more substantial system sizes.

arXiv:1809.05792Physical review. B./Physical review. BApr 23, 201958 citations

Decay of Correlations for Quantum Spin Systems with a Transverse Field: A Dynamic Approach

Alessandra Cipriani, Paolo Dai Pra

We consider a wide class of quantum spin systems obtained by adding a transverse field to a classical Hamiltonian. We give explicit high-temperature conditions which guarantee exponential decay of correlations. A stochastic-geometric representation allows to reformulate the model as a classical random field on a space of marked point processes on the circle $[0,β)$ , where $β$ is the inverse temperature. We then construct a Markov process having this random field as invariant measure. By the mixing properties of the process, the exponential decay of correlations follows by an adaptation of a general argument.We consider a wide class of quantum spin systems obtained by adding a transverse field to a classical Hamiltonian. We give explicit high-temperature conditions which guarantee exponential decay of correlations. A stochastic-geometric representation allows to reformulate the model as a classical random field on a space of marked point processes on the circle $[0,β)$, where $β$ is the inverse temperature. We then construct a Markov process having this random field as invariant measure. By the mixing properties of the process, the exponential decay of correlations follows by an adaptation of a general argument.

arXiv:1005.3547May 19, 20103 citations

Berry’s geometrical phases in ESR in the presence of a stochastic process

Dan Gamliel, Jack H. Freed

Berry's [Proc. R. Soc. London, Ser. A 392, 45 (1984)] geometrical phase is discussed in the context of dissipative evolution of an interacting spin system, governed by the stochastic Liouville equation. An analytical treatment is given for a possible ESR experiment on an interacting electron-nucleus system, modulated by two-site jumps. Geometrical phases are shown to be relevant to systems of this type, when their Hamiltonian changes slowly with time. A method for obtaining higher-order corrections to the adiabatic approximation is demonstrated. It is found that if the jumps are slow relative to the rate of change of the Hamiltonian, their effect reduces to familiar line broadening, and the geometrical phases may be observed experimentally. Equations are also set up for a similar ESR experiment on an electron-nucleus system undergoing isotropic rotational diffusion, and a brief discussion of the equations follows.Berry's [Proc. R. Soc. London, Ser. A 392, 45 (1984)] geometrical phase is discussed in the context of dissipative evolution of an interacting spin system, governed by the stochastic Liouville equation. An analytical treatment is given for a possible ESR experiment on an interacting electron-nucleus system, modulated by two-site jumps. Geometrical phases are shown to be relevant to systems of this type, when their Hamiltonian changes slowly with time. A method for obtaining higher-order corrections to the adiabatic approximation is demonstrated. It is found that if the jumps are slow relative to the rate of change of the Hamiltonian, their effect reduces to familiar line broadening, and the geometrical phases may be observed experimentally. Equations are also set up for a similar ESR experiment on an electron-nucleus system undergoing isotropic rotational diffusion, and a brief discussion of the equations follows.

Physical Review AApr 1, 198958 citations

[0,β)

, where

β

is the inverse temperature. We then construct a Markov process having this random field as invariant measure. By the mixing properties of the process, the exponential decay of correlations follows by an adaptation of a general argument.