The purpose of this paper is to present some simple variants of a recently developed iterative algorithm for improvement of any given trial wave function. These modifications improve the convergence rate of the iterative process and allow us to obtain a good variational state for larger lattices. We apply the method to the one-dimensional Gross-Neveu model with one flavor in a finite-size lattice. The ground-state energy, the density-density correlation function, and the single-particle Green's function are calculated. They are in good agreement with existing results.
We study variational preparation of ground states and sector-resolved excited states in the
(1+1)-dimensional lattice Gross-Neveu model. We construct fixed circuits preserving either total fermion number or every flavor number, and a problem-specific scalable-circuit adaptive variational quantum eigensolver (SC-ADAPT-VQE). Classical circuit benchmarks cover massless and massive systems through 30 qubits, using exact-diagonalization and tensor-network reference results. Imposing flavor-number conservation improves the achieved energies in the completed two-flavor comparisons. Selected massive fixed-ansatz benchmarks with one to four flavors have relative energy errors of approximately
1×10−5 -
2×10−4, smaller than the quoted literature errors where available, although discretizations and computational resources differ. The adaptive pool combines translated bulk and boundary-sensitive generators with an interaction-sensitive cross-flavor family. Selected massive SC-ADAPT benchmarks with one to three flavors have relative energy errors below
2.1×10−3. For one flavor, matrix-product-state evaluations extend the transferred circuits to 60-400 qubits without target-side operator selection or parameter optimization, giving energy deviations of approximately
0.35% -
1.76% from density-matrix renormalization-group reference values at maximum bond dimension 256. At fixed flavor number, range caps, and append count, the adaptive construction has a precompilation local-factor count linear in volume and a volume-independent shared-parameter count; fixed-accuracy performance at arbitrary volumes remains unestablished. Sequential deflation also prepares low-lying states within a fixed flavor-number sector, with projector fidelities providing a basis-independent assessment of degenerate target eigenspaces.
We present a spectroscopy scheme for the lattice field theory by using the tensor renormalization group method combining with the transfer matrix formalism. By using the scheme, we cannot only compute the energy spectrum for the lattice theory but also determine quantum numbers of the energy eigenstates. Furthermore, the wave function of the corresponding eigenstate can also be computed. The first step of the scheme is to coarse grain the tensor network of a given lattice model by using the higher order tensor renormalization group, and then after making a matrix corresponding to a transfer matrix from the coarse-grained tensors, its eigenvalues are evaluated to extract the energy spectrum. Second, the quantum number of the eigenstates can be identified by a selection rule that requires to compute matrix elements of an associated insertion operator. The matrix elements can be represented by an impurity tensor network and computed by the coarse-graining scheme. Moreover, we can compute the wave function of the energy eigenstate by putting the impurity tensor at each point in space direction of the network. Additionally, the momentum of the eigenstate can also be identified by computing appropriate matrix elements represented by the tensor network. As a demonstration of the new scheme, we show the spectroscopy of the ( 1 + 1 ) d Ising model and compare it with exact results. We also present a scattering phase shift obtained from two-particle state energy using Lüscher’s formula. Published by the American Physical Society 2024