arXiv subjects

J. M. P. Carmelo

Publications and source records attributed to J. M. P. Carmelo.

At least 19 recordsLinked to original sources

arXiv2026

Exact results for the Hubbard model on bipartite lattices in spatial dimensions $d>1$: Seven theorems from the full [SU(2)$\times$SU(2)$\times$U(1)]/$\mathbb{Z}_2^2$ symmetry

There are few exact results for the Hubbard model on bipartite lattices of spatial dimension $d>1$. Nevertheless, the Hubbard model with transfer integral $t$ and onsite repulsion $U$ on bipartite lattices with $N_a$ sites, such as the square, honeycomb, cubic, body-centered cubic, face-centered cubic, and diamond lattices, provides the simplest toy model for describing electronic correlations in many condensed-matter systems and is therefore a quantum problem of considerable physical interest. Seven exact theorems that provide new physical insight into the model are established. Overall, the exact framework based on physical spins and physical $η$-spins for the Hubbard model on bipartite lattices of spatial dimension $d>1$ introduced in this paper offers a robust foundation for future studies of the model, as well as of the condensed-matter materials, such as cuprate superconductors, graphene and graphene-derived systems, and other quantum systems, that it describes.

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arXiv2025

Finite-temperature transport in the gapped spin-1/2 XXZ chain and one-dimensional lattice spinless fermion model

Here we consider a class of energy eigenstates of the spin-1/2 XXZ chain that exist both for anisotropies 1 and larger than 1. We show that at the isotropic point their contributions are behind the diffusion constant being infinite, spin transport being anomalous superdiffusive for temperatures T>0. That for anisotropy larger than 1 such states do not contribute to the diffusion constant is shown to imply it is finite, spin transport being normal diffusive for T>0. By combining the connection through a Jordan-Wigner transformation of the spin-1/2 XXZ chain to the one-dimensional (1D) lattice spinless fermion model at zero chemical potential for V/J larger or equal to 1 with its Bethe-ansatz solution, where V is the nearest-neighbor Coulomb repulsion and J is twice the hopping integrai, in this paper we also address the issue of the T>0 charge transport of that model at zero chemical potential. It is found to be anomalous superdiffusive for V/J=1 and normal diffusive for V/J>1.

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arXiv2025

Diffusive charge transport in the gapped 1D Hubbard model at all finite temperatures

Studies relying on hydrodynamic theory and Kardar-Parisi-Zhang (KPZ) scaling have found that in the one-dimensional Hubbard model spin and charge transport are for all temperatures T > 0 anomalous superdiffusive at zero magnetic field, h = 0, and zero chemical potential, μ = 0, respectively. However, this contradicts recent exact results that at very low temperature charge transport rather is normal diffusive. In this Letter we identify the mechanisms that control the different types of temperature dependence of the h = 0 spin and μ = 0 charge transport and find that the latter is normal diffusive for all finite temperatures T > 0, in contrast to the hydrodynamic theory and KPZ scaling predictions.

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arXiv2025

Ising spin-1/2 XXZ chain's quantum problems beyond the spinon paradigm

Spin chains are correlated quantum models of great interest in quantum systems and materials exhibiting quasi-one-dimensional magnetic properties. Here we review results on quantum problems associated with spin chains that are beyond the usual spinon paradigm. In this review we consider two quantum problems that are beyond the spinon representation: (a) Spin Bethe strings of length n that have no spinon representation, contribute to the dynamical properties of the spin-1/2 XXZ chain with anisotropy larger than 1 and for n=1,2,3 were experimentally identified and realized in the zigzag materials SrCo2V2O8 and BaCo2V2O8; (b) The spin stiffness associated with ballistic spin transport at arbitrary finite temperature, which involves a huge number of energy eigenstates, many of which are generated in the thermodynamic limit from ground states by an infinite number of elementary processes.

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arXiv2025

Finite-temperature charge and spin transport in the one-dimensional Hubbard model accounting for its global [SU (2) X SU(2) X U(1)]/Z_2^2$ symmetry

Using a general representation that accounts for the effects on finite-temperature spin and charge transport of the global [SU (2) X SU(2) X U(1)]/(Z2 X Z2) symmetry of the one-dimensional (1D) Hubbard model, we show that important finite-temperature transport quantities as the finite-field spin and finite-chemical potential charge stiffnesses and the zero-field spin and zero-chemical potential charge diffusion constants are controlled by microscopic processes associated with the spin and charge elementary currents carried by the spin and charge carriers, respectively. We describe the model finite-temperature transport properties in terms of the microscopic processes associated with the spin and charge elementary currents carried by the corresponding carriers. We expect that the general representation used in our study is that suitable to address the open problems on finite-temperature transport in the 1D Hubbard model also discussed in this paper.

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arXiv2024

Temperature dependence of charge transport in the half-filled 1D Hubbard model

The use of hydrodynamic transport theory seems to indicate that the charge diffusion constant D of the one-dimensional (1D) half-filled Hubbard model, whose Drude weight vanishes, diverges for temperature T>0, which would imply anomalous superdiffusive charge transport. Here the leading term of that constant is derived for low finite temperatures much smaller than the the Mott-Hubbard gap. It only diverges in the temperature infinite limit, being finite and decreasing upon increasing T within the low-temperature regime. Our exact results both provide valuable physical information ona complex quantum problem and bring about the interesting unsolved issue of how charge transport evolves from normal diffusive for low temperatures to anomalous superdiffusive in the infinite temperature limit.

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arXiv2023

Zigzag materials: selective interchain couplings control the coexistence of one-dimensional physics and deviations from it

The coexistence in the low-temperature spin-conducting phases of the zigzag materials BaCo2V2O8 and SrCo2V2O8 of one-dimensional (1D) physics with important deviations from it is not well understood. The studies of this paper account for an important selection rule that follows from interchain spin states being coupled more strongly within the spin dynamical structure factor of such zigzag materials whenever they are connected by a specific symmetry operation of the underlying lattice. In the case of excited states, this symmetry operation is only a symmetry in spin-space ifno electronic spin flip is performed within the generation of such states. Our results on both the role of selective interchain couplings in protecting the 1D physics and being behind deviations from it and on the dynamical properties being controlled by scattering of singlet pairs of physical spins 1/2 open the door to a key advance in the understanding of the physics of the spin chains in BaCo2V2O8 and SrCo2V2O8.

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arXiv2020

Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain

Recently there has been a renewed interest in the spectra and role in dynamical properties of excited states of the spin-1/2 Heisenberg antiferromagnetic chain in longitudinal magnetic fields associated with Bethe strings. The latter are bound states of elementary magnetic excitations described by Bethe-ansatz complex non-real rapidities. Previous studies on this problem referred to finite-size systems. Here we consider the thermodynamic limit and study it for the isotropic spin-1/2 Heisenberg XXX chain in a longitudinal magnetic field. We confirm that also in that limit the most significant spectral weight contribution from Bethe strings leads to gapped continua in the spectra of the spin +- and xx dynamical structure factors. The contribution of Bethe strings to the zz dynamical structure factor is found to be small at low spin densities and to become negligible upon increasing that density above 0.317. For the -+ dynamical structure factor, that contribution is found to be negligible at finite magnetic field. We derive analytical expressions for the line shapes of the +-, xx, and zz dynamical structure factors valid in the vicinity of singularities located at and just above the gapped lower thresholds of the Bethe-string states's spectra. As a side result and in order to provide an overall physical picture that includes the relative location of all spectra with a significant amount of spectral weight, we revisit the general problem of the line-shape of the transverse and longitudinal spin dynamical structure factors at finite magnetic field and excitation energies in the vicinity of other singularities. This includes those located at and just above the lower thresholds of the spectra that stem from excited states described by only real Bethe-ansatz rapidities.

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arXiv2019

Effects of finite-range interactions on the one-electron spectral properties of one-dimensional metals: Application to Bi/InSb(001)

We study the one-electron spectral properties of one-dimensional interacting electron systems in which the interactions have finite range. We employ a mobile quantum impurity scheme that describes the interactions of the fractionalized excitations at energies above the standard Tomonga-Luttinger liquid limit and show that the phase shifts induced by the impurity describe universal properties of the one-particle spectral function. We find the explicit forms in terms of these phase shifts for the momentum dependent exponents that control the behavior of the spectral function near and at the (k,omega)-plane singularities where most of the spectral weight is located. The universality arises because the line shape near the singularities is independent of the short-distance part of the interaction potentials. For the class of potentials considered here, the charge fractionalized particles have screened Coulomb interactions that decay with a power-law exponent l>5. We apply the theory to the angle-resolved photo-electron spectroscopy (ARPES) in the highly one-dimensional bismuth-induced anisotropic structure on indium antimonide Bi/InSb(001). Our theoretical predictions agree quantitatively with both (i) the experimental value found in Bi/InSb(001) for the exponent alpha that controls the suppression of the density of states at very small excitation energy omega and (ii) the location in the (k,omega) plane of the experimentally observed high-energy peaks in the ARPES momentum and energy distributions. We conclude with a discussion of experimental properties beyond the range of our present theoretical framework and further open questions regarding the one-electron spectral properties of Bi/InSb(001).

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arXiv2019

One-particle spectral function singularities in a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction

The momentum, fermionic density, spin density, and interaction dependencies of the exponents that control the (momentum-energy)-plane singular features of the one-fermion spectral functions of a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction both at zero and finite magnetic field are studied in detail. Our results refer to energy scales beyond the reach of the low-energy Tomonaga-Luttinger liquid and rely on the pseudofermion dynamical theory for integrable models. The one-fermion spectral weight distributions associated with the spectral functions studied in this paper may be observed in systems of spin-1/2 ultra-cold fermionic atoms in optical lattices.

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arXiv2018

Pseudoparticle approach to 1D integrable quantum models

Over the last three decades a large number of experimental studies on several quasi one-dimensional (1D) metals and quasi1D Mott-Hubbard insulators have produced evidence for distinct spectral features identified with charge-only and spin-only fractionalized particles. They can be also observed in ultra-cold atomic 1D optical lattices a nd quantum wires. 1D exactly solvable models provide nontrivial tests of the approaches for these systems relying on field theories. Different schemes such as the pseudofermion dynamical theory (PDT) and the mobile quantum impurity model (MQIM) have revealed that the 1D correlated models high-energy physics is qualitatively different from that of a low-energy Tomonaga-Luttinger liquid (TLL). This includes the momentum dependence of the exponents that control the one- and two-particle dynamical correlation functions near their spectra edges and in the vicinity of one-particle singular spectral features. On the one hand, the low-energy charge-only and spin-only fractionalized particles are usually identified with holons and spinons, respectively. On the other hand, `particle-like' representations in terms of {\it pseudoparticles}, related PDT {\it pseudofermions}, and MQIM particles are suitable for the description of both the low-energy TLL physics and high-energy spectral and dynamical properties of 1D correlated systems. The main goal of this review is to revisit the usefulness of pseudoparticle and PDT pseudofermion representations for the study of both static and high-energy spectral and dynamical properties of the 1D Lieb-Liniger Bose gas, spin-$1/2$ isotropic Heisenberg chain, and 1D Hubbard model. Moreover, the relation between the PDT and the MQIM is clarified.

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arXiv2018

Absence of ballistic charge transport in the half-filled 1D Hubbard model

Whether in the thermodynamic limit of lattice length infinite, hole concentration tending to zero, nonzero temperature, and U/t > 0 the charge stiffness of the 1D Hubbard model with first neighbor transfer integral t and on-site repulsion U is finite or vanishes and thus whether there is or there is no ballistic charge transport, respectively, remains an unsolved and controversial issue, as different approaches yield contradictory results. In this paper we provide an upper bound on the charge stiffness and show that (similarly as at zero temperature), for T >0 and U/t>0 it vanishes in the limit of zero hole concentration within the canonical ensemble in the thermodynamic limit. Moreover, we show that at high temperature the charge stiffness vanishes as well within the grand-canonical ensemble in the infinite lattice length limit and chemical potential approaching half the Mott-Hubbard gap. The lack of charge ballistic transport indicates that charge transport at finite temperatures is dominated by a diffusive contribution. Our scheme uses a suitable exact representation of the electrons in terms of rotated electrons for which the numbers of singly occupied and doubly occupied lattice sites are good quantum numbers for U/t>0. In contrast to often less controllable numerical studies, the use of such a representation reveals the carriers that couple to the charge probes and provides useful physical information on the microscopic processes behind the exotic charge transport properties of the 1D electronic correlated system under study.

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arXiv2016

Absence of high-temperature ballistic transport in the spin-$1/2$ $XXX$ chain within the grand-canonical ensemble

Whether in the thermodynamic limit, vanishing magnetic field $h\rightarrow 0$, and nonzero temperature the spin stiffness of the spin-$1/2$ $XXX$ Heisenberg chain is finite or vanishes within the grand-canonical ensemble remains an unsolved and controversial issue, as different approaches yield contradictory results. Here we provide an upper bound on the stiffness and show that within that ensemble it vanishes for $h\rightarrow 0$ in the thermodynamic limit of chain length $L\to\infty$, at high temperatures $T\rightarrow\infty$. Our approach uses a representation in terms of the $L$ physical spins $1/2$. For all configurations that generate the exact spin-$S$ energy and momentum eigenstates such a configuration involves a number $2S$ of unpaired spins $1/2$ in multiplet configurations and $L-2S$ spins $1/2$ that are paired within $M_{\rm sp}=L/2-S$ spin-singlet pairs. The Bethe-ansatz strings of length $n=1$ and $n>1$ describe a single unbound spin-singlet pair and a configuration within which $n$ pairs are bound, respectively. In the case of $n>1$ pairs this holds both for ideal and deformed strings associated with $n$ complex rapidities with the same real part. The use of such a spin $1/2$ representation provides useful physical information on the problem under investigation in contrast to often less controllable numerical studies. Our results provide strong evidence for the absence of ballistic transport in the spin-$1/2$ $XXX$ Heisenberg chain in the thermodynamic limit, for high temperatures $T\to\infty$, vanishing magnetic field $h\rightarrow 0$ and within the grand-canonical ensemble.

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arXiv2016

One-electron singular spectral features of the 1D Hubbard model at finite magnetic field

The momentum, electronic density, spin density, and interaction dependences of the exponents that control the $(k,ω)$-plane singular features of the $σ=\uparrow,\downarrow$ one-electron spectral functions of the 1D Hubbard model at finite magnetic field are studied. The usual half-filling concepts of one-electron lower Hubbard band and upper Hubbard band are defined for all electronic density and spin density values and the whole finite repulsion range in terms of the rotated electrons associated with the model Bethe-ansatz solution. Such rotated electrons are the link of the non-perturbative relation between the electrons and the pseudofermions. Our results further clarify the microscopic processes through which the pseudofermion dynamical theory accounts for the $σ$ one-electron matrix elements between the ground state and excited energy eigenstates.

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arXiv2015

Dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field

We study the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds of the leading-order dominant excitations. We derive the exact momentum and spin-density dependences of the exponents controlling the singularities for both the longitudinal and transversal dynamical structure factors for the whole momentum range, in the thermodynamic limit. In that limit we argue that the higher-order excitations change neither the exponents nor the sharpness of the singularities. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal.

cond-mat.str-el↗

arXiv2015

Vanishing spin stiffness in the spin-1/2 Heisenberg chain for any nonzero temperature

Whether at zero spin density $m=0$ and finite temperatures $T>0$ the spin stiffness of the spin-$1/2$ $XXX$ chain is finite or vanishes remains an unsolved and controversial issue, as different approaches yield contradictory results. Here we provide an exact upper bound on the stiffness within a canonical ensemble at any fixed value of spin density $m$ and show that it is proportional to $m^2 L$ in the thermodynamic limit of chain length $L\to\infty$, for any finite, nonzero temperature. Moreover, we explicitly compute the stiffness at $m=0$ and confirm that it vanishes. This allows us to exactly exclude the possibility of ballistic transport within the canonical ensemble for $T>0$.

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arXiv2013

Elementary objects of the 1D Hubbard model

Exotic elementary objects such as "holons" and "spinons", which are widely used in descriptions of correlated electrons in reduced spatial dimensions, were introduced from analysis of the excitation branches of one-dimensional (1D) models. The 1D Hubbard model with effective nearest-neighbor hopping integral t and on-site repulsion U is a prominent example. In the last twenty years a large number of angle-resolved photoemission spectroscopy experiments as well as electron energy-loss spectroscopic studies and high-resolution resonant inelastic X-ray experiments on several quasi-1D metals and quasi-1D Mott-Hubbard insulators have observed separate charge and spin spectral features, which have been identified with "holons" and "spinons". The elementary objects emerging within non-perturbative 1D correlated systems play now the same role in actual low-dimensional materials as Fermi-liquid quasiparticles in three-dimensional metals. The main goal of this paper is the review of representations of the 1D Hubbard model physics in terms of elementary objects whose configurations generate the energy eigenstates from the electron or hole vacuum. In addition, the relation to the holon and spinon representations is discussed and clarified.

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arXiv2013

1D Hubbard model elementary objects scattering

In terms of electron processes, the 1D Hubbard model is a nonperturbative problem. That renders the description in terms of electron scattering of the microscopic processes that control the model properties a very difficult task. In this paper we study the corresponding scattering processes of the elementary objects whose occupancy configurations generate the energy eigenstates from the electron vacuum. Due to the related occurrence of an infinite set of conservation laws associated with the model integrability, such objects are found to undergo only zero-momentum forward-scattering collisions. The description of the model dynamical properties in terms of such elementary objects scattering events then drastically simplifies. The corresponding 1D Hubbard model scattering theory refers to arbitrary values of the densities and finite repulsive interaction U>0. Each ground-state - excited-state transition is associated with a well defined set of elementary zero-momentum forward-scattering events. The elementary-object scatterers dressed S matrix is expressed as a commutative product of S matrices, each corresponding to a two-object scattering event. This commutative factorization is stronger than the factorization associated with Yang-Baxter equation for the original spin-1/2 electron bare S matrix. The power-law singularities exponents in the finite-energy correlation-functions of the metallic phases of a wide class of 1D integrable and non-integrable systems are momentum dependent. In the present exactly solvable model such an exponent momentum dependence is controlled by the phase shifts and corresponding dressed S matrix considered in this paper.

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