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arXiv:2110.15856 · Physical review. B./Physical review. B

Fate of pairing and spin-charge separation in the presence of long-range antiferromagnetism

Luhang Yang, Ignacio J. Hamad, L. O. Manuel, Adrian E. Feiguin

Published May 5, 2022• 3 citations
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Abstract

We present a numerical study of competing orders in the 1D $t\text{\ensuremath{-}}J$ model with long-range RKKY-like staggered spin interactions. By circumventing the constraints imposed by Mermin-Wagner's theorem, this Hamiltonian can realize long-range N\'eel order at half filling. We determine the full phase diagram as a function of the exchange and particle density using the density matrix renormalization group (DMRG) method. We show that pairing is disfavored and the AFM insulator and metallic phases are separated by a broad regime with phase segregation, before spin-charge separation re-emerges at low densities. Upon doping, interactions induce a confining potential that binds holons and spinons into full fledged fermionic quasiparticles in a range of parameters and densities. We numerically calculate the photoemission spectrum of the model, showing the appearance of a coherent quasiparticle band splitting away from the holon-spinon continuum with a width determined by $J$ that survives at finite doping. Comparison with analytical results using the self-consistent Born approximation (SCBA) and by solving the spinon-holon problem offer insight into the internal structure of the quasiparticles and help us explain the different features in the spectrum. We discuss how this simple toy model can teach us about the phenomenology of its higher-dimensional counterpart.

DOI
10.1103/physrevb.105.195104

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We present a numerical study of competing orders in the 1D t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model with long-range RKKY-like staggered spin interactions. By circumventing the constraints imposed by Mermin-Wagner's theorem, this Hamiltonian can realize long-range N'eel order at half filling. We determine the full phase diagram as a function of the exchange and particle density using the density matrix renormalization group (DMRG) method. We show that pairing is disfavored and the AFM insulator and metallic phases are separated by a broad regime with phase segregation, before spin-charge separation re-emerges at low densities. Upon doping, interactions induce a confining potential that binds holons and spinons into full fledged fermionic quasiparticles in a range of parameters and densities. We numerically calculate the photoemission spectrum of the model, showing the appearance of a coherent quasiparticle band splitting away from the holon-spinon continuum with a width determined by JJJ that survives at finite doping. Comparison with analytical results using the self-consistent Born approximation (SCBA) and by solving the spinon-holon problem offer insight into the internal structure of the quasiparticles and help us explain the different features in the spectrum. We discuss how this simple toy model can teach us about the phenomenology of its higher-dimensional counterpart.
Decades after the discovery of high-temperature superconductivity, understanding the effects of doping a Mott insulator remains a topic of great relevance, since the fundamental excitations in the normal state are not known, nor the precise origin of the pairing mechanism. In particular, the nature of the pseudogap phase at finite temperatures, above the superconducting dome, or the redistribution of spectral weight observed in experiments indicate that our knowledge is incomplete and theories may be missing some key ingredients.Due to the two-dimensionality of the problem and the limitations imposed by the Mermin-Wagner theorem, the numerical study of these questions is remarkably difficult: most treatments are either limited to small or quasi one-dimensional systems at zero temperature, or simulations may be carried out at finite temperature, completely missing the possibility for long-range order. In this dissertation, we tackle paradigmatic problems in condensed matter from a fundamentally new perspective. We numerically study interacting chains and ladders introducing RKKY-like SU(2)-symmetric long-range interactions that allow one to realize actual spontaneous symmetry breaking and true antiferromagnetic order. We shed new light on problems such as the role of magnetic order on quasi-particle formation and fractionalization, and pairing instabilities in generalized Hubbard-like models. In particular, we address questions of a very fundamental nature: (i) How do spinons evolve into magnons and what are their signatures in the excitation spectrum? (ii) how do coherent quasi-particles form in the presence of long range order? Will we still observe signatures of spin-charge separation in the spectrum? (iii) what is the interplay between long-range antiferromagnetic order and pairing? Our work offers new insight onto the role played by long-range antiferromagnetism in quasi-particle formation and pairing in the context of new toy-models that realize much of the phenomenology of their higher dimensional counterparts.--Author's abstract
A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a T2{\mathit{T}}^{2}T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.
We study the nature of the excitations of an antiferromagnetic (AFM) Heisenberg chain with staggered long range interactions using the time-dependent density matrix renormalization group method and by means of a multi-spinon approximation. The chain undergoes true symmetry breaking and develops long range order, transitioning from a gapless spin liquid to a gapless ordered AFM phase. The spin dynamic structure factor shows that the emergence of Néel order can be associated to the formation of bound states of spinons that become coherent magnons. The quasiparticle band leaks out from the two-spinon continuum that is pushed up to higher energies. Our physical picture is also supported by an analysis of the behavior of the excitations in real-time.
We introduce a slave-fermion formulation in which to study the charge dynamics of the half-filled Hubbard model on the square lattice. In this description, the charge degrees of freedom are represented by fermionic holons and doublons and the Mott-insulating characteristics of the ground state are the consequence of holon–doublon bound-state formation. The bosonic spin degrees of freedom are described by the antiferromagnetic Heisenberg model, yielding long-ranged (Néel) magnetic order at zero temperature. Within this framework and in the self-consistent Born approximation, we perform systematic calculations of the average double occupancy, the electronic density of states, the spectral function and the optical conductivity. Qualitatively, our method reproduces the lower and upper Hubbard bands, the spectral-weight transfer into a coherent quasiparticle band at their lower edges and the renormalisation of the Mott gap, which is associated with holon–doublon binding, due to the interactions of both quasiparticle species with the magnons. The zeros of the Green function at the chemical potential give the Luttinger volume, the poles of the self-energy reflect the underlying quasiparticle dispersion with a spin-renormalised hopping parameter and the optical gap is directly related to the Mott gap. Quantitatively, the square-lattice Hubbard model is one of the best-characterised problems in correlated condensed matter and many numerical calculations, all with different strengths and weaknesses, exist with which to benchmark our approach. From the semi-quantitative accuracy of our results for all but the weakest interaction strengths, we conclude that a self-consistent treatment of the spin-fluctuation effects on the charge degrees of freedom captures all the essential physics of the antiferromagnetic Mott–Hubbard insulator. We remark in addition that an analytical approximation with these properties serves a vital function in developing a full understanding of the fundamental physics of the Mott state, both in the antiferromagnetic insulator and at finite temperatures and dopings.
The physical nature of doped Mott insulators has been the subject of intensive study for decades. The single-band Hubbard model and the $t\text{\ensuremath{-}}J$ model on a bipartite lattice are widely recognized as the simplest models to describe these materials. However, the key mechanism of superconductivity in these toy models remains unclear. Here we propose a novel mechanism for the (d+idd+idd+id)-wave superconductivity (SC) that occurs in the small-doping region of the honeycomb lattice $t\text{\ensuremath{-}}J$ model based on the Grassmann tensor product state numerical simulation and spin-charge separation formulation. In the presence of anti-ferromagnetic order near half-filling, we develop a continuum effective field theory for holons, which reveals the competition between repulsive and attractive holon interactions induced by spinon fluctuations and gauge fluctuations, respectively. When t/Jt/Jt/J is large, the repulsive interaction dominates, leading to a non-Fermi liquid behavior; while in a moderate range of t/Jt/Jt/J, the attractive interaction dominates, leading to the SC order. Potential theoretical and experimental methods to validate the mechanism are discussed.
The physical nature of doped Mott-insulator has been intensively studied for more than three decades. It is well known that the single band Hubbard model or ttt-JJJ model on the bipartite lattice is the simplest model to describe a doped Mott insulator. Unfortunately, the key mechanism of superconductivity in these toy models is still under debate. In this paper, we propose a new mechanism for the d+idd+idd+id-wave superconductivity (SC) that occurs in the small-doping region of the honeycomb lattice ttt-JJJ model based on the Grassmann tensor product state numerical simulation and spin-charge separation formulation. Moreover, in the presence of anti-ferromagnetic order, a continuum effective field theory for holons is developed near half-filling. It reveals the competition between repulsive and attractive holon interactions induced by spinon fluctuations and gauge fluctuations, respectively. At a large value of t/Jt/Jt/J, the repulsive interaction dominates, leading to the non-Fermi liquid like behavior; while in a moderate range of t/Jt/Jt/J, the attractive interaction dominates, leading to the SC order. Possible experimental detection of spin-charge separation phenomena is also discussed.