SciPost Phys. 10, 019 (2021) ·
published 28 January 2021

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Within the tensor network framework, the (positive) thermal density operator
can be approximated by a double layer of infinite Projected Entangled Pair
Operator (iPEPO) coupled via ancilla degrees of freedom. To investigate the
thermal properties of the spin1/2 Heisenberg model on the square lattice, we
introduce a family of fully spin$SU(2)$ and lattice$C_{4v}$ symmetric onsite
tensors (of bond dimensions $D=4$ or $D=7$) and a plaquettebased
TrotterSuzuki decomposition of the imaginarytime evolution operator. A
variational optimization is performed on the plaquettes, using a full (for
$D=4$) or simple (for $D=7$) environment obtained from the singlesite Corner
Transfer Matrix Renormalization Group fixed point. The method is benchmarked by
a comparison to quantum Monte Carlo in the thermodynamic limit. Although the
iPEPO spin correlation length starts to deviate from the exact exponential
growth for inversetemperature $\beta \gtrsim 2$, the behavior of various
observables turns out to be quite accurate once plotted w.r.t the inverse
correlation length. We also find that a direct $T=0$ variational energy
optimization provides results in full agreement with the
$\beta\rightarrow\infty$ limit of finitetemperature data, hence validating the
imaginarytime evolution procedure. Extension of the method to frustrated
models is described and preliminary results are shown.
SciPost Phys. 7, 041 (2019) ·
published 2 October 2019

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We consider a family of SU(2)symmetric Projected Entangled Paired States
(PEPS) on the square lattice, defining coloredResonating Valence Bond (RVB)
states, to describe the quantum disordered phase of the $J_1J_2$ frustrated
Heisenberg model.For $J_2/J_1\sim 0.55$ we show the emergence of critical
(algebraic) dimerdimer correlations  typical of RokhsarKivelson (RK) points
of quantum dimer models on bipartite lattices  while, simultaneously, the
spinspin correlation length remains short. Our findings are consistent with a
spin liquid or a weak Valence Bond Crystal in the neighborhood of an RK point.
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