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references

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• Shastry–Sutherland Model

  1. Exact Dimer Ground State of the Two Dimensional Heisenberg Spin System $\text{SrCu}_2(\text{BO}_3)_2$

     • discuss about exact ground state

  2. Quantum Criticality and Spin Liquid Phase in the Shastry-Sutherland model

     • focusing on the $g = J_D/J_{\times}, g \in [0.7, 0.9]$, with DMRG calculation.

  3. Tensor network study of the Shastry-Sutherland model in zero magnetic field

     • tensor network study

  4. Signatures of the finite-temperature mirror symmetry breaking in the $S=1/2$ Shastry-Sutherland model

     • use canonical thermal pure quantum (TPQ)
     • also, The ground state phase diagram is listed.

  5. Dynamics and Instabilities of the Shastry-Sutherland Model

  • apply magnetic field
  6. Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations
     • Check "negative sign problem" part.

• Majumder-gohsh

  1. Exact ground states of frustrated quantum spin systems consisting of spin-dimer units
  2. Nakamura, Tota, Satoshi Takada, Kiyomi Okamoto, and Naoki Kurosawa. 1997. “Haldane and Dimer Gap in General Double Spin-Chain Models.” arXiv [cond-Mat]. arXiv. http://arxiv.org/abs/cond-mat/9702182.

• ladder model

  1. Multiple magnetization plateaus induced by farther neighbor interaction in an S=1 two-leg Heisenberg spin ladder

  2. Efficient Quantum Monte Carlo simulations of highly frustrated magnets: the frustrated spin-1/2 ladder

     • can remove negative sign at fully frustrated parameter point ($J_\times = J_\parallel$) by local unitary transformation.

• Kitaev model

  1. An introduction to Kitaev model-I

  2. Anyons in an exactly solved model and beyond

  • original paper of kitaev.

  3. Theory of the Kitaev model in a [111] magnetic field

     • summerizing several methods for simulating Kitaev model (DMRG, tensor-network)

  4. Majorana-magnon crossover by a magnetic field in the Kitaev model:Continuous-time quantum Monte Carlo study

     • simulate with QMC.

• pyrochlore lattice

  1. Monte Carlo study of the discontinuous quantum phase transition in the transverse-field Ising model on the pyrochlore lattice

• Negative sign problem

  1. Symmetry-protected topological order and negative-sign problem for SO(N) bilinear-biquadratic chains

     • With a generalized Jordan-Wigner transformation, bilinear-biquadratic(BLBQ) spin chain could be negative-sign free

  2. Sign-Problem-Free Monte Carlo Simulation of Certain Frustrated Quantum Magnets

     • The scheme uses the basis of total spin eigenstates of clusters of spins to avoid the severe sign problem faced by other QMC methods.

  3. Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations

     • Also discuss about Shastry-Surtherland model
     • If the Hamiltonian of interest and the sign-problem-free Hamiltonian have the same ground state and this state is a member of the computational basis, then the average sign returns to one as the temperature goes to zero.

  4. Reduction of the sign problem near T = 0 in quantum Monte Carlo simulations

     • solve negative-sign problem near T = 0 using the above rule.

  5. Mitigating the Sign Problem through Basis Rotations

     • optimize over the choice of basis for sign-free quantum Monte-Carlo simulations using the idea of (ⅲ).

• cluster algorithm

  1. Cluster Algorithms for General-S Quantum Spin Systems

  2. Markov Chain Monte Carlo Method without Detailed Balance

     • As name suggests, this algorithm minimize the average rejection rate, and even reduced to zero in many relevant cases.

  3. Geometric Allocation Approach for Transition Kernel of Markov Chain

     • algorithm for constructing rejection free transition kernel that satisfies detai balance condition. Just symmetric version of $\rm(ii)$

• frustration-free model

  1. Multiple magnetization plateaus induced by farther neighbor interaction in an $S = 1$ two-leg Heisenberg spin ladder
     • Consider the interaction that couples up to the nextnearest neighbor rungs and find an exactly solvable regime where the ground states become product states.

• reweighting

  1. Nakamura, Tota, Naomichi Hatano, and Hidetoshi Nishimori. 1992. “Reweighting Method for Quantum Monte Carlo Simulations with the Negative-Sign Problem.” Journal of the Physical Society of Japan 61 (10): 3494–3502.
     • Studying J1J2 model with quantum monte carlo algorithm. Note that trotter number is finite here, which means there is systematical bias for calculation.
  2. Hatano, Naomichi. 1994. “Data Analysis for Quantum Monte Carlo Simulations with the Negative-Sign Problem.” Journal of the Physical Society of Japan 63 (5): 1691–97.
     • Data analysis for reweighting method. Particulally this paper refer to the distribution of ratio of expectation value.