Ravi Teja Ponnaganti, Matthieu Mambrini, Didier Poilblanc
SciPost Phys. 15, 158 (2023) ·
published 12 October 2023

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Within the Projected Entangled Pair State (PEPS) tensor network formalism, a simple update (SU) method has been used to investigate the time evolution of a twodimensional U(1) critical spin1/2 spin liquid under Hamiltonian quench [Phys. Rev. B 106, 195132 (2022)]. Here we introduce two different variational frameworks to describe the time dynamics of SU(2)symmetric translationallyinvariant PEPS, aiming to improve the accuracy. In one approach, after using a TrotterSuzuki decomposition of the time evolution operator in term of twosite elementary gates, one considers a single bond embedded in an environment approximated by a Corner Transfer Matrix Renormalization Group (CTMRG). A variational update of the two tensors on the bond is performed under the application of the elementary gate and then, after symmetrization of the site tensors, the environment is updated. In the second approach, a cluster optimization is performed on a finite (periodic) cluster, maximizing the overlap of the exact timeevolved state with a symmetric finitesize PEPS ansatz. Observables are then computed on the infinite lattice contracting the infinitePEPS (iPEPS) by CTMRG. We show that the variational schemes outperform the SU method and remain accurate over a significant time interval before hitting the entanglement barrier. Studying the spectrum of the transfer matrix, we find that the asymptotic correlations are very well preserved under time evolution, including the critical nature of the singlet correlations, as expected from the LiebRobinson (LR) bound theorem. Consistently, the system (asymptotic) boundary is found to be described by the same Conformal Field Theory of central charge $c = 1$ during time evolution. We also compute the timeevolution of the short distance spinspin correlations and estimate the LR velocity.
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.