Ground-state phase diagram of the two-dimensional t-J model

Abstract

The ground-state phase diagram of the two-dimensional t − J model is investigated in the context of the tensor network algorithm in terms of the graded Projected Entangled-Pair State representation of the ground-state wave functions. There is a line of phase separation between the Heisenberg anti-ferromagnetic state without hole and a hole-rich state. For both J = 0.4t and J = 0.8t, a systematic computation is performed to identify all the competing ground states for various dopings. It is found that, besides a possible Nagaoka's ferromagnetic state, the homogeneous regime consists of four different phases: one phase with charge and spin density wave order coexisting with a p x (p y )−wave superconducting state, one phase with the symmetry mixing of d + s−wave superconductivity in the spin-singlet channel and p x (p y )−wave superconductivity in the spin-triplet channel in the presence of an anti-ferromagnetic background, one superconducting phase with extended s−wave symmetry, and one superconducting phase with p x (p y )−wave symmetry in a ferromagnetic background.

Generalized Hartree–Fock theory for interacting fermions in lattices: numerical methods

“…[13,14]. The results are obviously less precise than those obtained with such methods, other Monte Carlo approaches [15], or the recently developed algorithms based on PEPS and other tensor networks states [16][17][18][19][20][21]. Although we obtain a good qualitative agreement with [13,14] in many regimes, the FGS are, as expected, not able to capture all possible fermionic phases in the strong-correlation regimes, as they constitute a subclass of all possible fermionic states.…”

Tensor Network States and Geometry

“…The projected entangled-pair state (PEPS) [21][22][23][24][25][26][27][28][29][30] generalizes the MPS, whereas D > 1 versions of TTN 31,32 and MERA [33][34][35][36][37][38][39] also exist. Among those generalizations, PEPS and MERA stand out for offering efficient representations of many-body wave functions, thus leading to scalable simulations in D > 1 dimensions; and, importantly, for also being able to address systems that are beyond the reach of quantum Monte Carlo approaches due to the so-called sign problem, including frustrated spins 30,39 and interacting fermions [40][41][42][43][44][45][46][47][48][49][50] .…”

Fermionic implementation of projected entangled pair states algorithm

“…Inner rows, on the other hand, cannot be represented as matrix product operators in a form which would allow immediate contraction with matrix product states due to the fermionic signs produced by reordering vertical virtual fermionic operators. Nevertheless, using the fact that the parity of K i,j is determined globally by the underlying operator O i,j , one can change the contraction order in contracting first two rows to (19) where f = n i=1 p 1i i−1 j=1 p 2j . Note that this step is trivial since there is no need for fermionic swap rules as no fermionic modes are crossed.…”

“…The first fPEPS simulations albeit without the sign-free contraction rules, were performed in Refs. 18,19 under the name Graded PEPS, and very promising numerical results were reported. Finally, the full sign-free fPEPS algorithm for infinite lattices was implemented, together with interesting numerical results on interacting fermions and the t-J model, in Ref.…”