Critical properties of the exact density of states for discrete systems

Tiago Mendes-Santos, Giuliano Giudici, Marcello Dalmonte +1 more

We consider a lattice version of the Bisognano-Wichmann (BW) modular Hamiltonian as an ansatz for the bipartite entanglement Hamiltonian of the quantum critical chains. Using numerically unbiased methods, we check the accuracy of the BW ansatz by both comparing the BW R\'enyi entropy to the exact results and investigating the size scaling of the norm distance between the exact reduced density matrix and the BW one. Our study encompasses a variety of models, scanning different universality classes, including integrable models such as the transverse field Ising, three-state Potts and XXZ chains, and the nonintegrable bilinear-biquadratic model. We show that the R\'enyi entropies obtained via the BW ansatz properly describe the scaling properties predicted by conformal field theory. Remarkably, the BW R\'enyi entropies also faithfully capture the corrections to the conformal field theory scaling associated with the energy density operator. In addition, we show that the norm distance between the discretized BW density matrix and the exact one asymptotically goes to zero with the system size: this indicates that the BW ansatz also can be employed to predict properties of the eigenvectors of the reduced density matrices and is thus potentially applicable to other entanglement-related quantities such as negativity.

Leo Stodolsky, J. Wosiek

Muhammad Shaeer Moeed, Tobias Serwatka, Pierre–Nicholas Roy

Typical path integral Monte Carlo approaches use the primitive approximation to compute the probability density for a given path. In this work, we develop the pair discrete variable representation (pair-DVR) approach to study molecular rotations. The pair propagator, which was initially introduced to study superfluidity in condensed helium, is naturally well-suited for systems interacting with a pairwise potential. Consequently, paths sampled using the pair action tend to be closer to the exact paths (compared to primitive Trotter paths) for such systems leading to convergence with less imaginary time steps. Our approach relies on using the pair factorization approach in conjunction with a discretized path integral ground state paradigm to study a chain of planar rotors interacting with a pairwise dipole interaction. We first use the Wigner-Kirkwood density expansion to analyze the asymptotics of the pair propagator in imaginary time. Then, we exhibit the utility of the pair factorization scheme via convergence studies comparing the pair and primitive propagators. Finally, we compute energetic and structural properties of this system including the correlation function and Binder ratio as functions of the coupling strength to examine the behavior of the pair-DVR method near criticality. The density matrix renormalization group results are used for benchmarking throughout.

Robert Hosken

Hisatoshi Yokoyama, Masao Ogata

Ground-state properties of the one-dimensional t-J model are studied by using exact diagonalization of small systems and compared with those found with Gutzwiller-Jastrow--type variational functions. Near the supersymmetric case (J/t=2), the Gutzwiller wave function is an extremely good trial function for all electron densities. It reproduces momentum distribution and correlation functions of the exact ground state except for critical behaviors. For J/t2 (>2), the ground-state properties are well described by Jastrow functions with repulsive (attractive) intersite correlations.

Amnon Aharony A