Efficient tensor network representation for Gutzwiller projected states of paired fermions

Abstract

Recent work by Wu et al. [arXiv:1910.11011] proposed a numerical method, so called MPO-MPS method, by which several types of quantum many-body wave functions, in particular, the projected Fermi sea state, can be efficiently represented as a tensor network. In this paper, we generalize the MPO-MPS method to study Gutzwiller projected paired states of fermions, where the maximally localized Wannier orbitals for Bogoliubov quasiparticles/quasiholes have been adapted to improve the computational performance. The study of S O(3)symmetric spin-1 chains reveals that this new method has better performance than variational Monte Carlo for gapped states and similar performance for gapless states. Moreover, we demonstrate that dynamic correlation functions can be easily evaluated by this method cooperating with other MPS-based accurate approaches, such as the Chebyshev MPS method. arXiv:2001.04611v1 [cond-mat.str-el]

Tensor Renormalization Group for interacting quantum fields

“…Therefore, since the former has a diagrammatic expansion so it does the latter. As shown in (39) the logarithm of F 1 only contains connected Feynman diagrams. Expression (53) makes clear that this property is also inherited by f 1 .…”

“…The argument of the exponential represents a connected Feynman diagram with four legs contributing at first order in perturbation theory. It has the same structure as the last graph in (39). The splitting of the previous term according to (50)…”

Unveiling the S=3/2 Kitaev Honeycomb Spin Liquids

“…The connection to the S=1/2 KHM indicates that in particular the ferromagnetic QSLs will be very fragile and, in general, the formation of conventional magnetic order will be further facilitated because of flux-fermion boundstate formation involving the almost flat Majorana bands. In that context, the quality of our parton mean-field states can be further improved by efficient tensor network representation with Gutzwiller projection [57][58][59] or by including different flux sectors in the variational ansatz [60].…”

Unveiling a critical stripy state in the triangular-lattice SU(4) spin-orbital model

“…In this Letter, we reexamine the ground state of the SU(4) KK model on the triangular lattice by combining the DMRG method [52,53] with Gutzwiller projected wave function approach. Our recent methodology development [54][55][56] provides a useful tool for converting Gutzwiller projected wave functions into matrix product states (MPSs) and exploiting them to boost DMRG calculations and characterize ground states. With two complementary methods and extensive numerical efforts, we have gathered clear evidence for a critical stripy ground state for the SU(4) KK model on the triangular lattice.…”

“…where r i is the column index of lattice site i, r j ≥ r i is assumed for NN bond i j , and δ ∈ Thanks to the newly developed method [54,55], the ground states of Hamiltonians ( 3) and ( 4) can be represented as MPSs, upon which the Gutzwiller projection can be easily implemented to impose the single-occupancy constraint and obtain many-body wave functions in the physical spin-orbital Hilbert space. These trial wave functions, in their MPS form, can be used to initialize DMRG calculations, which is dubbed as "Gutzwiller-boosted DMRG" [56].…”