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arXiv:cond-mat/9705128

DMRG Study of the Striped Phase in the 2D t-J model

Steven R. White, Douglas J. Scalapino

Published May 14, 1997• 5 citations
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Abstract

Using the density matrix renormalization group (DMRG), we study the 2D t-J model at a hole doping of x=1/8 on clusters as large as 19x8. We find a striped phase which is consistent with recent neutron scattering experiments. We find that bond-centered and site-centered stripes have nearly the same energy, suggesting that in the absence of pinning effects the domain walls can fluctuate.

DOI
10.48550/arxiv.cond-mat/9705128

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Using the density matrix renormalization group (DMRG), we study the 2D t-J model at a hole doping of x=1/8 on clusters as large as 19x8. We find a striped phase which is consistent with recent neutron scattering experiments. We find that bond-centered and site-centered stripes have nearly the same energy, suggesting that in the absence of pinning effects the domain walls can fluctuate.
Using the density matrix renormalization group, we study the 2D $t\ensuremath{-}J$ model at a hole doping of x=18x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{8}x=81​ on clusters as large as $19\ifmmode\times\else\texttimes\fi{}8$. We find a striped phase consistent with recent neutron scattering experiments. We find that bond-centered and site-centered stripes have nearly the same energy, suggesting that in the absence of pinning effects the domain walls can fluctuate.
Using the density matrix renormalization group, we calculate the energy of a domain wall in the 2D $t\ensuremath{-}J$ model as a function of the linear hole density ${\ensuremath{\rho}}_{\ensuremath{\ell}}$, as well as the interaction energy between walls, for J/t=0.35J/t\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.35J/t=0.35. Based on these results, we conclude that the ground state always has domain walls for dopings $0<x\ensuremath{\lesssim}0.3$. For $x\ensuremath{\lesssim}0.125$, the system has (1, 0) domain walls with ${\ensuremath{\rho}}_{\ensuremath{\ell}}\ensuremath{\sim}0.5$, while for $0.125\ensuremath{\lesssim}x\ensuremath{\lesssim}0.17$ the system has a possibly phase-separated mixture of walls with ${\ensuremath{\rho}}_{\ensuremath{\ell}}\ensuremath{\sim}0.5$ and ${\ensuremath{\rho}}_{\ensuremath{\ell}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$. For $x\ensuremath{\gtrsim}0.17$, there are only walls with ${\ensuremath{\rho}}_{\ensuremath{\ell}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$.
Using the density matrix renormalization group, we study domain wall structures in the t-J model at a hole doping of x=1/8. We find that the domain walls are composed of d_{x^2-y^2} pairs and that the regions between the domain walls have antiferromagnetic correlations that are pi phase shifted across a domain wall. At x=1/8, the hole filling corresponds to one hole per two domain wall unit cells. When the pairs in a domain wall are pinned by an external field, the d_{x^2-y^2} pairing response is suppressed, but when the pinning is weakened, d_{x^2-y^2} pair-field correlations can develop.
We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t-[Formula: see text]-J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negative [Formula: see text] values ([Formula: see text]) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The [Formula: see text] (hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we find [Formula: see text] strongly suppresses superconductivity. The [Formula: see text] (electron-doped) region shows the expected circular Fermi pocket of holes around the [Formula: see text] point and a broad low-doped region of coexisting antiferromagnetism and d-wave pairing with a triplet p component at wavevector [Formula: see text] induced by the antiferromagnetism and d-wave pairing. The pairing for the electron low-doped system with [Formula: see text] is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker d-wave pairing and striped p-wave pairing appears. In a small doping region near [Formula: see text] for [Formula: see text], we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders.
The ground state of a hole-doped t-t'-J ladder with four legs favors a striped charge distribution. Spin excitation from the striped ground state is known to exhibit incommensurate spin excitation near q=(pi,pi) along the leg direction (qx direction). However, an outward dispersion from the incommensurate position toward q=(0,pi) is strong in intensity, inconsistent with inelastic neutron scattering (INS) experiment in hole-doped cuprates. Motivated by this inconsistency, we use the t-t'-J model with m x n=96 lattice sites by changing lattice geometry from four-leg (24x4) to rectangle (12x8) shape and investigate the dynamical spin structure factor by using the dynamical density matrix renormalization group. We find that the outward dispersion has weak spectral weights in the 12x8 lattice, accompanied with the decrease of excitation energy close to q=(pi,pi), being consistent with the INS data. In the 12x8 lattice, weakening of incommensurate spin correlation is realized even in the presence of the striped charge distribution. For further investigation of geometry related spin dynamics, we focus on direction dependent spin excitation reported by recent resonant inelastic x-ray scattering (RIXS) for cuprate superconductors and obtain a consistent result with RIXS by examining an 8x8 t-t'-J square lattice.