Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Topological ground-state excitations and symmetry in the many-electron one-dimensional problem

J. M. P. Carmelo, Nuno M. R. Peres

Published Jan 1, 1995• 1 citation
OpenAlex

Abstract

We consider the Hubbard chain in a magnetic field and chemical potential. We introduce a pseudohole basis where all states are generated from a single reference vacuum. This allows the evaluation for all sectors of Hamiltonian symmetry of the model of the expression of the σ electron and hole operators at Fermi momentum ±kFσ and vanishing excitation energy in terms of pseudohole operators. In all sectors and to leading order in the excitation energy the electron and hole are constituted by one c pseudohole, one s pseudohole, and one topological momenton. These three quantum objects are confined in the electron or hole and cannot be separated. We find that the set of different pseudohole types which in pairs constitute the two electrons and two holes associated with the transitions from the (N↑,N↓) ground state to the (N↑+1,N↓), (N↑,N ↓ +1) and (N ↑ −1,N↓), (N↑,N ↓ −1) ground states, respectively, transform in the representation of the symmetry group of the Hamiltonian in the initial-ground-state sector of parameter space. We also find the pseudohole generators for the half-filling holon and zero-magnetic-field spinon. The pseudohole basis introduced in this paper is the only suitable for the extension of the present type of operator description to the whole Hilbert space. 1 I.

Related papers

Complete pseudohole and heavy-pseudoparticle operator representation for the Hubbard chain

J. M. P. Carmelo, Nuno M. R. Peres

We introduce the pseudohole and heavy-pseudoparticle operator algebra that generates all Hubbard-chain eigenstates from a single reference vacuum. In addition to the pseudoholes already introduced for the description of the low-energy physics, this involves the heavy pseudoparticles associated with Hamiltonian eigenstates whose energy spectrum has a gap relative to the many-electron ground state. We introduce a generalized pseudoparticle perturbation theory that describes the relevant finite-energy ground-state transitions. In the present basis these excitations refer to a small density of excited pseudoparticles. Our operator basis goes beyond the Bethe-ansatz solution and it is the suitable and correct starting point for the study of the finite-frequency properties, which are of great relevance for the understanding of the unusual spectral properties detected in low-dimensional novel materials.

arXiv:cond-mat/9701094•Physical review. B, Condensed matter•Aug 15, 1997•16 citations

Ground states of integrable quantum liquids

J. M. P. Carmelo, Nuno M. R. Peres

Based on a recently introduced operator algebra for the description of a class of integrable quantum liquids we define the ground states for all canonical ensembles of these systems. We consider the particular case of the Hubbard chain in a magnetic field and chemical potential. The ground states of all canonical ensembles of the model can be generated by acting on the electron vacuum (densities n1) or hole vacuum (densities n>1), with suitable pseudoparticle creation operators. We also evaluate the energy gaps of the non-lowest-weight states and non-highest-weight states of the \ensuremath{\eta} spin and spin algebras relative to the corresponding ground states. For all sectors of parameter space and symmetries the exact ground state of the many-electron problem is in the pseudoparticle basis the noninteracting pseudoparticle ground state. This plays a central role in the pseudoparticle perturbation theory.

arXiv:cond-mat/9411096•Physical review. B, Condensed matter•Mar 15, 1995•5 citations

GROUND-STATE PROPERTIES AND ELEMENTARY EXCITATIONS OF THE ONE-DIMENSIONAL HUBBARD MODEL

J. M. P. Carmelo, D. Baeriswyl

The ground state of the one-dimensional Hubbard Hamiltonian is discussed on the basis of the Bethe ansatz solution of Lieb and Wu. A simple analytical representation of the distribution functions for charge and spin degrees of freedom is derived. The elementary excitations are associated with electron-hole pairs of two pseudo-fermion systems, one for the charge, the other for the magnetic excitations. Spinons and holons correspond to ground state configurations of odd-numbered rings. It is argued that holons will form bound pairs in weakly coupled chains.

International Journal of Modern Physics B•Oct 1, 1988•7 citations

Electrons, pseudoparticles, and quasiparticles in the one-dimensional many-electron problem

J. M. P. Carmelo, A. H. Castro Neto

We generalize the concept of quasiparticle for one-dimensional (1D) interacting electronic systems. The \ensuremath{\uparrow} and \ensuremath{\downarrow} quasiparticles recombine the pseudoparticle colors c and s (charge and spin at zero-magnetic field) and are constituted by one many-pseudoparticle topological-momentum shift and one or two pseudoparticles. These excitations cannot be separated. We consider the case of the Hubbard chain. We show that the low-energy electron-quasiparticle transformation has a singular character which justifies the perturbative and nonperturbative nature of the quantum problem in the pseudoparticle and electronic basis, respectively. This follows from the absence of zero-energy electron-quasiparticle overlap in 1D. The existence of Fermi-surface quasiparticles both in 1D and three dimensional (3D) many-electron systems suggests their existence in quantum liquids in dimensions 1D3. However, whether the electron-quasiparticle overlap can vanish in D>1 or whether it becomes finite as soon as we leave 1D remains an unsolved question. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9604155•Physical review. B, Condensed matter•Oct 15, 1996•4 citations

Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries

Valentin Zauner-Stauber, Laurens Vanderstraeten, Jutho Haegeman +2 more

We develop variational matrix product state (MPS) methods with symmetries to determine dispersion relations of one-dimensional quantum lattices as a function of momentum and preset quantum number. We test our methods on the XXZ spin chain, the Hubbard model, and a nonintegrable extended Hubbard model and determine the excitation spectra with a precision similar to the one of the ground state. The formulation in terms of quantum numbers makes the topological nature of spinons and holons very explicit. In addition, the method also enables an easy and efficient direct calculation of the necessary magnetic field or chemical potential required for a certain ground state magnetization or particle density.

arXiv:1802.07197•Physical review. B./Physical review. B•Jun 29, 2018•43 citations

Exact solution of thet-Jmodel in one dimension at 2t=±J: Ground state and excitation spectrum

P.-A. Bares, G. Blatter, Masao Ogata

The one dimensional t-J Hamiltonian is diagonalized exactly for the supersymmetric case 2t=\ifmmode\pm\else\textpm\fi{}J using the Bethe ansatz. In this limit it is identical with models previously considered by Lai, Sutherland, and Schlottmann. In the present paper we discuss the ground-state properties and excitation spectrum in zero magnetic field. The ground state is a liquid of singlet bonds with varying spatial separation. Its most remarkable feature is the presence of bonds connecting particles at arbitrarily large distances. The ground-state energy is an analytic function of the band filling. There is no difference in the chemical potential for adding one or two particles and no evidence for the binding of holes. The low-lying part of the spectrum consists of two types of gapless excitations (charge and spin) with effective Fermi surfaces at 2${\mathit{k}}_{\mathit{F}}$ and ${\mathit{k}}_{\mathit{F}}$, respectively. An interpretation of the energy spectrum in terms of spinons and holons is appropriate at low energies.

Physical review. B, Condensed matter•Jul 1, 1991•182 citations
We consider the Hubbard chain in a magnetic field and chemical potential. We introduce a pseudohole basis where all states are generated from a single reference vacuum. This allows the evaluation for all sectors of Hamiltonian symmetry of the model of the expression of the σ electron and hole operators at Fermi momentum ±kFσ and vanishing excitation energy in terms of pseudohole operators. In all sectors and to leading order in the excitation energy the electron and hole are constituted by one c pseudohole, one s pseudohole, and one topological momenton. These three quantum objects are confined in the electron or hole and cannot be separated. We find that the set of different pseudohole types which in pairs constitute the two electrons and two holes associated with the transitions from the (N↑,N↓) ground state to the (N↑+1,N↓), (N↑,N ↓ +1) and (N ↑ −1,N↓), (N↑,N ↓ −1) ground states, respectively, transform in the representation of the symmetry group of the Hamiltonian in the initial-ground-state sector of parameter space. We also find the pseudohole generators for the half-filling holon and zero-magnetic-field spinon. The pseudohole basis introduced in this paper is the only suitable for the extension of the present type of operator description to the whole Hilbert space. 1 I.
We introduce the pseudohole and heavy-pseudoparticle operator algebra that generates all Hubbard-chain eigenstates from a single reference vacuum. In addition to the pseudoholes already introduced for the description of the low-energy physics, this involves the heavy pseudoparticles associated with Hamiltonian eigenstates whose energy spectrum has a gap relative to the many-electron ground state. We introduce a generalized pseudoparticle perturbation theory that describes the relevant finite-energy ground-state transitions. In the present basis these excitations refer to a small density of excited pseudoparticles. Our operator basis goes beyond the Bethe-ansatz solution and it is the suitable and correct starting point for the study of the finite-frequency properties, which are of great relevance for the understanding of the unusual spectral properties detected in low-dimensional novel materials.
Based on a recently introduced operator algebra for the description of a class of integrable quantum liquids we define the ground states for all canonical ensembles of these systems. We consider the particular case of the Hubbard chain in a magnetic field and chemical potential. The ground states of all canonical ensembles of the model can be generated by acting on the electron vacuum (densities n1) or hole vacuum (densities n>1), with suitable pseudoparticle creation operators. We also evaluate the energy gaps of the non-lowest-weight states and non-highest-weight states of the \ensuremath{\eta} spin and spin algebras relative to the corresponding ground states. For all sectors of parameter space and symmetries the exact ground state of the many-electron problem is in the pseudoparticle basis the noninteracting pseudoparticle ground state. This plays a central role in the pseudoparticle perturbation theory.
The ground state of the one-dimensional Hubbard Hamiltonian is discussed on the basis of the Bethe ansatz solution of Lieb and Wu. A simple analytical representation of the distribution functions for charge and spin degrees of freedom is derived. The elementary excitations are associated with electron-hole pairs of two pseudo-fermion systems, one for the charge, the other for the magnetic excitations. Spinons and holons correspond to ground state configurations of odd-numbered rings. It is argued that holons will form bound pairs in weakly coupled chains.
We generalize the concept of quasiparticle for one-dimensional (1D) interacting electronic systems. The \ensuremath{\uparrow} and \ensuremath{\downarrow} quasiparticles recombine the pseudoparticle colors c and s (charge and spin at zero-magnetic field) and are constituted by one many-pseudoparticle topological-momentum shift and one or two pseudoparticles. These excitations cannot be separated. We consider the case of the Hubbard chain. We show that the low-energy electron-quasiparticle transformation has a singular character which justifies the perturbative and nonperturbative nature of the quantum problem in the pseudoparticle and electronic basis, respectively. This follows from the absence of zero-energy electron-quasiparticle overlap in 1D. The existence of Fermi-surface quasiparticles both in 1D and three dimensional (3D) many-electron systems suggests their existence in quantum liquids in dimensions 1D3. However, whether the electron-quasiparticle overlap can vanish in D>1 or whether it becomes finite as soon as we leave 1D remains an unsolved question. \textcopyright{} 1996 The American Physical Society.
We develop variational matrix product state (MPS) methods with symmetries to determine dispersion relations of one-dimensional quantum lattices as a function of momentum and preset quantum number. We test our methods on the XXZ spin chain, the Hubbard model, and a nonintegrable extended Hubbard model and determine the excitation spectra with a precision similar to the one of the ground state. The formulation in terms of quantum numbers makes the topological nature of spinons and holons very explicit. In addition, the method also enables an easy and efficient direct calculation of the necessary magnetic field or chemical potential required for a certain ground state magnetization or particle density.
The one dimensional t-J Hamiltonian is diagonalized exactly for the supersymmetric case 2t=\ifmmode\pm\else\textpm\fi{}J using the Bethe ansatz. In this limit it is identical with models previously considered by Lai, Sutherland, and Schlottmann. In the present paper we discuss the ground-state properties and excitation spectrum in zero magnetic field. The ground state is a liquid of singlet bonds with varying spatial separation. Its most remarkable feature is the presence of bonds connecting particles at arbitrarily large distances. The ground-state energy is an analytic function of the band filling. There is no difference in the chemical potential for adding one or two particles and no evidence for the binding of holes. The low-lying part of the spectrum consists of two types of gapless excitations (charge and spin) with effective Fermi surfaces at 2kF{\mathit{k}}_{\mathit{F}}kF​ and kF{\mathit{k}}_{\mathit{F}}kF​, respectively. An interpretation of the energy spectrum in terms of spinons and holons is appropriate at low energies.