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Register a new userProjected entangled pair states study of anisotropic-exchange magnets on triangular lattice
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The anisotropic-exchange spin-1/2 model on a triangular lattice has been used to describe the rare-earth chalcogenides, which may have exotic ground states. We investigate the quantum phase diagram of the model by using the projected entangled pair state (PEPS) method, and compare it to the classical phase diagram. Besides two stripe-ordered phase, and the 120$^circ$ state, there is also a multi-textbf{Q} phase. We identify the multi-textbf{Q} phase as a $Z_{2}$ vortex state. No quantum spin liquid state is found in the phase diagram, contrary to the previous DMRG calculations.
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We analyze a criterion which guarantees that the ground states of certain many body systems are stable under perturbations. Specifically, we consider PEPS, which are believed to provide an efficient description, based on local tensors, for the low energy physics arising from local interactions. In order to assess stability in the framework of PEPS, one thus needs to understand how physically allowed perturbations of the local tensor affect the properties of the global state. In this paper, we show that a restricted version of the Local Topological Quantum Order (LTQO) condition provides a checkable criterion which allows to assess the stability of local properties of PEPS under physical perturbations. We moreover show that LTQO itself is stable under perturbations which preserve the spectral gap, leading to nontrivial examples of PEPS which possess LTQO and are thus stable under arbitrary perturbations.
Variational Monte Carlo studies employing projected entangled-pair states (PEPS) have recently shown that they can provide answers on long-standing questions such as the nature of the phases in the two-dimensional $J_1 - J_2$ model. The sampling in these Monte Carlo algorithms is typically performed with Markov Chain Monte Carlo algorithms employing local update rules, which often suffer from long autocorrelation times and interdependent samples. We propose a sampling algorithm that generates independent samples from a PEPS, bypassing all problems related to finite autocorrelation times. This algorithm is a generalization of an existing direct sampling algorithm for unitary tensor networks. We introduce an auxiliary probability distribution from which independent samples can be drawn, and combine it with importance sampling in order to evaluate expectation values accurately. We benchmark our algorithm on the classical Ising model and on variational optimization of two-dimensional quantum spin models.
The recently developed stochastic gradient method combined with Monte Carlo sampling techniques [PRB {bf 95}, 195154 (2017)] offers a low scaling and accurate method to optimize the projected entangled pair states (PEPS). We extended this method to the fermionic PEPS (fPEPS). To simplify the implementation, we introduce a fermi arrow notation to specify the order of the fermion operators in the virtual entangled EPR pairs. By defining some local operation rules associated with the fermi arrows, one can implement fPEPS algorithms very similar to that of standard PEPS. We benchmark the method for the interacting spinless fermion models, and the t-J models. The numerical calculations show that the gradient optimization greatly improves the results of simple update method. Furthermore, much larger virtual bond dimensions ($D$) and truncation dimensions ($D_c$) than those of boson and spin systems are necessary to converge the results. The method therefore offer a powerful tool to simulate fermion systems because it has much lower scaling than the direct contraction methods.
We present a scheme to perform an iterative variational optimization with infinite projected entangled-pair states (iPEPS), a tensor network ansatz for a two-dimensional wave function in the thermodynamic limit, to compute the ground state of a local Hamiltonian. The method is based on a systematic summation of Hamiltonian contributions using the corner transfer-matrix method. Benchmark results for challenging problems are presented, including the 2D Heisenberg model, the Shastry-Sutherland model, and the t-J model, which show that the variational scheme yields considerably more accurate results than the previously best imaginary time evolution algorithm, with a similar computational cost and with a faster convergence towards the ground state.
We investigate thermodynamic properties like specific heat $c_{V}$ and susceptibility $chi$ in anisotropic $J_1$-$J_2$ triangular quantum spin systems ($S=1/2$). As a universal tool we apply the finite temperature Lanczos method (FTLM) based on exact diagonalization of finite clusters with periodic boundary conditions. We use clusters up to $N=28$ sites where the thermodynamic limit behavior is already stably reproduced. As a reference we also present the full diagonalization of a small eight-site cluster. After introducing model and method we discuss our main results on $c_V(T)$ and $chi(T)$. We show the variation of peak position and peak height of these quantities as function of control parameter $J_2/J_1$. We demonstrate that maximum peak positions and heights in Neel phase and spiral phases are strongly asymmetric, much more than in the square lattice $J_1$-$J_2$ model. Our results also suggest a tendency to a second side maximum or shoulder formation at lower temperature for certain ranges of the control parameter. We finally explicitly determine the exchange model of the prominent triangular magnets Cs$_2$CuCl$_4$ and Cs$_{2}$CuBr$_{4}$ from our FTLM results.
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