skip to main content


The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 5:00 PM ET until 11:00 PM ET on Friday, June 21 due to maintenance. We apologize for the inconvenience.

Title: Ground-state phase diagram of the t-t ′ -J model

We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t-t-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 negativetvalues (t/t=±0.2) 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. Thet<0(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 findt<0strongly suppresses superconductivity. Thet>0(electron-doped) region shows the expected circular Fermi pocket of holes around the(π,π)point and a broad low-doped region of coexisting antiferromagnetism and d-wave pairing with a triplet p component at wavevector(π,π)induced by the antiferromagnetism and d-wave pairing. The pairing for the electron low-doped system witht>0is 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 nearx=0.08fort0.2, 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.

more » « less
Award ID(s):
Author(s) / Creator(s):
; ;
Publisher / Repository:
Proceedings of the National Academy of Sciences
Date Published:
Journal Name:
Proceedings of the National Academy of Sciences
Page Range / eLocation ID:
Article No. e2109978118
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D)3He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum,Lz=(N/2), forN/2Cooper pairs. The power law suppression of the angular momentum,Lz(T)(N/2)[123(πT/Δ)2]for0TTc, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid3He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry atDc216ξ0. The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement lengthDDc2. The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral ‘polar phase’ atDc19ξ0, in which a single p-wave orbital state of Cooper pairs is aligned along the channel.

    more » « less
  2. In the physics of condensed matter, quantum critical phenomena and unconventional superconductivity are two major themes. In electron-doped cuprates, the low critical field (HC2) allows one to study the putative quantum critical point (QCP) at low temperature and to understand its connection to the long-standing problem of the origin of the high-TCsuperconductivity. Here we present measurements of the low-temperature normal-state thermopower (S) of the electron-doped cuprate superconductor La2−xCexCuO4(LCCO) fromx= 0.11–0.19. We observe quantum criticalS/Tversusln(1/T)behavior over an unexpectedly wide doping rangex= 0.15–0.17 above the QCP (x= 0.14), with a slope that scales monotonically with the superconducting transition temperature (TCwith H = 0). The presence of quantum criticality over a wide doping range provides a window on the criticality. The thermopower behavior also suggests that the critical fluctuations are linked withTC. Above the superconductivity dome, atx= 0.19, a conventional Fermi-liquidSTbehavior is found forT40 K.

    more » « less
  3. We present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat-band superconductors that lead to upper bounds for the superfluid stiffness and the two-dimensional (2D)Tc. We focus on on-site attraction|U|on the Lieb lattice with trivial flat bands and on the π-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weightD̃lowñ|U|Ω/2withñ=minn,2n, where n is the flat-band density and Ω is the Marzari–Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound forD̃lowlinear in|U|. We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte Carlo results.

    more » « less
  4. Abstract

    Magnetic reconnection is often invoked as a source of high-energy particles, and in relativistic astrophysical systems it is regarded as a prime candidate for powering fast and bright flares. We present a novel analytical model—supported and benchmarked with large-scale three-dimensional kinetic particle-in-cell simulations in electron–positron plasmas—that elucidates the physics governing the generation of power-law energy spectra in relativistic reconnection. Particles with Lorentz factorγ≳ 3σ(here,σis the magnetization) gain most of their energy in the inflow region, while meandering between the two sides of the reconnection layer. Their acceleration time istaccγηrec1ωc120γωc1, whereηrec≃ 0.06 is the inflow speed in units of the speed of light andωc=eB0/mcis the gyrofrequency in the upstream magnetic field. They leave the region of active energization aftertesc, when they get captured by one of the outflowing flux ropes of reconnected plasma. We directly measuretescin our simulations and find thattesctaccforσ≳ few. This leads to a universal (i.e.,σ-independent) power-law spectrumdNfree/dγγ1for the particles undergoing active acceleration, anddN/dγγ2for the overall particle population. Our results help to shed light on the ubiquitous presence of power-law particle and photon spectra in astrophysical nonthermal sources.

    more » « less
  5. The explicit breaking of the axial symmetry by quantum fluctuations gives rise to the so-called axial anomaly. This phenomenon is solely responsible for the decay of the neutral pion π0into two photons (γγ), leading to its unusually short lifetime. We precisely measured the decay width Γ of theπ0 γγprocess. The differential cross sections for π0photoproduction at forward angles were measured on two targets, carbon-12 and silicon-28, yieldingΓ(π0 γγ)=7.798±0.056(stat.)±0.109(syst.) eV, where stat. denotes the statistical uncertainty and syst. the systematic uncertainty. We combined the results of this and an earlier experiment to generate a weighted average ofΓ(π0 γγ)=7.802±0.052(stat.)±0.105(syst.) eV. Our final result has a total uncertainty of 1.50% and confirms the prediction based on the chiral anomaly in quantum chromodynamics.

    more » « less