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arXiv:cond-mat/9405064 · Physical review. B, Condensed matter

Mechanism of spin and charge separation in one-dimensional quantum antiferromagnets

Christopher Mudry, Eduardo Fradkin

Published Oct 15, 1994• 52 citations
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Abstract

We reconsider the problem of separation of spin and charge in one-dimensional quantum antiferromagnets. We show that spin and charge separation in one-dimensional strongly correlated systems cannot be described by the slave-boson or fermion representation within any perturbative treatment of the interactions between the slave holons and slave spinons. The constraint of single occupancy must be implemented exactly. As a result the slave fermions and bosons are not part of the physical spectrum. Instead, the excitations that carry the separate spin and charge quantum numbers are solitons. To prove this result, it is sufficient to study the pure spinon sector in the slave-boson representation. We start with a short-range resonating-valence-bond state spin liquid mean-field theory for the frustrated antiferromagnetic spin-1/2 chain. We derive an effective theory for the fluctuations of the Affleck-Marston and Anderson order parameters. We show how to recover the phase diagram as a function of the frustration by treating the fluctuations nonperturbatively.

DOI
10.1103/physrevb.50.11409

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In this paper we reexamine the problem of the separation of spin and charge degrees of freedom in two-dimensional strongly correlated systems. We establish a set of sufficient conditions for the occurrence of spin and charge separation. Specifically, we discuss this issue in the context of the Heisenberg model for spin-1/2 on a square lattice with nearest (${\mathit{J}}_{1}$) and next-nearest (${\mathit{J}}_{2}$) neighbor antiferromagnetic couplings. Our formulation makes explicit the existence of a local SU(2) gauge symmetry once the spin-1/2 operators are replaced by bound states of spinons. The mean-field theory for the spinons is solved numerically as a function of the ratio ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$ for the so-called s-RVB ansatz (s-RVB stands for short range resonating valence bond). A second-order phase transition exists in a flux state for ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$ larger than the critical value (${\mathit{J}}_{2/}$${\mathit{J}}_{1}$${)}_{\mathrm{cr}}$ identify the range 0${\mathit{J}}_{2}$/${\mathit{J}}_{1}$(${\mathit{J}}_{2}$/${\mathit{J}}_{1}$${)}_{\mathrm{cr}}$ as the s-RVB phase. It is characterized by the existence of a finite gap to the elementary excitations (spinons) and the breakdown of all the continuous gauge symmetries. An effective continuum theory for the spinons and the gauge degrees of freedom is constructed just below the onset of the flux phase. We argue that this effective theory is consistent with the deconfinement of the spinons carrying the fundamental charge of the gauge group. We contrast this result with the study of the one-dimensional quantum antiferromagnet within the same approach. We show that in the one-dimensional model, the spinons of the gauge picture are always confined and thus cannot be identified with the gapless spin-1/2 excitations of the quantum antiferromagnet Heisenberg model.

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Spin and charge go their separate ways

Jelena Stajic

Quantum Simulation Strongly interacting chains of fermions are predicted to exhibit two types of collective excitations: spinons, which carry only spin, and holons, which carry only charge. These excitations move at different velocities. Signatures of this so-called spin-charge separation have been observed in solid-state systems, but obtaining direct dynamical evidence is tricky. With this goal in mind, Vijayan et al. perturbed a chain of ultracold interacting fermions housed in a one-dimensional optical lattice by removing one of the atoms. This gave rise to two independent excitations, which the researchers identified as spinons and holons using a quantum gas microscope. Science , this issue p. [186][1] [1]: /lookup/doi/10.1126/science.aay2354

Science•Jan 9, 2020•0 citations
We reconsider the problem of separation of spin and charge in one-dimensional quantum antiferromagnets. We show that spin and charge separation in one-dimensional strongly correlated systems cannot be described by the slave-boson or fermion representation within any perturbative treatment of the interactions between the slave holons and slave spinons. The constraint of single occupancy must be implemented exactly. As a result the slave fermions and bosons are not part of the physical spectrum. Instead, the excitations that carry the separate spin and charge quantum numbers are solitons. To prove this result, it is sufficient to study the pure spinon sector in the slave-boson representation. We start with a short-range resonating-valence-bond state spin liquid mean-field theory for the frustrated antiferromagnetic spin-1/2 chain. We derive an effective theory for the fluctuations of the Affleck-Marston and Anderson order parameters. We show how to recover the phase diagram as a function of the frustration by treating the fluctuations nonperturbatively.
In this paper we reexamine the problem of the separation of spin and charge degrees of freedom in two-dimensional strongly correlated systems. We establish a set of sufficient conditions for the occurrence of spin and charge separation. Specifically, we discuss this issue in the context of the Heisenberg model for spin-1/2 on a square lattice with nearest (J1{\mathit{J}}_{1}J1​) and next-nearest (J2{\mathit{J}}_{2}J2​) neighbor antiferromagnetic couplings. Our formulation makes explicit the existence of a local SU(2) gauge symmetry once the spin-1/2 operators are replaced by bound states of spinons. The mean-field theory for the spinons is solved numerically as a function of the ratio J2{\mathit{J}}_{2}J2​/J1{\mathit{J}}_{1}J1​ for the so-called s-RVB ansatz (s-RVB stands for short range resonating valence bond). A second-order phase transition exists in a flux state for J2{\mathit{J}}_{2}J2​/J1{\mathit{J}}_{1}J1​ larger than the critical value (J2/{\mathit{J}}_{2/}J2/​J1{\mathit{J}}_{1}J1​)cr{)}_{\mathrm{cr}})cr​ identify the range 0J2{\mathit{J}}_{2}J2​/J1{\mathit{J}}_{1}J1​(J2{\mathit{J}}_{2}J2​/J1{\mathit{J}}_{1}J1​)cr{)}_{\mathrm{cr}})cr​ as the s-RVB phase. It is characterized by the existence of a finite gap to the elementary excitations (spinons) and the breakdown of all the continuous gauge symmetries. An effective continuum theory for the spinons and the gauge degrees of freedom is constructed just below the onset of the flux phase. We argue that this effective theory is consistent with the deconfinement of the spinons carrying the fundamental charge of the gauge group. We contrast this result with the study of the one-dimensional quantum antiferromagnet within the same approach. We show that in the one-dimensional model, the spinons of the gauge picture are always confined and thus cannot be identified with the gapless spin-1/2 excitations of the quantum antiferromagnet Heisenberg model.
A fermion-spin transformation is used to implement the charge-spin separation, and is developed to study the low-dimensional t-J model. In this approach, the charge and spin degrees of freedom of the physical electron are separated, and the charge degree of freedom is represented by a spinless fermion while the spin degree of freedom is representd by a hard-core boson. The on-site local constraint for single occupancy is satisfied even in the mean-field approximation and the sum rule for the physical electron is obeyed. This approach can be applied to both one and two-dimensional systems. In the one-dimensional case, the spinon as well as the physical electron behave like Luttinger liquids. We have obtained a gapless charge and spin excitation spectrum, a good ground state energy, and a reasonable electron-momentum distribution within the mean-field approximation. The correct exponents of the correlation functions and momentum distribution are also obtained if the squeezing effect and rearrangement of the spin configurations are taken into account. In the two-dimensional case, within the mean-field approximation the magnetized flux state with a gap in the spinon spectrum has the lowest energy at half filling. The antiferromagnetic long-range order is destroyed by hole doping of the order \ensuremath{\sim}10-15 % for t/J=3-5 and a disordered flux state with gapless spinon spectrum becomes stable. The calculated specific heat is roughly consistent with observed results on copper oxide superconductors. The possible phase separation is also discussed at the mean-field level.
The mechanism of the charge-spin separation (CSS) in the t-J model, both in the slave-boson and the slave-fermion representations, is studied in detail from the viewpoint of gauge theory. The dynamics of the composite gauge bosons, i.e., of phase degrees of freedom of mean fields defined on links, is carefully analyzed. The Polyakov-Sussskind theory of the confinement-deconfinement (CD) phase transition plays an essential role in this analysis. As we showed generally in our previous paper, the CSS phase corresponds to the deconfinement phase of gauge theory of the mean field. The quasiparticles here are holons, spinons, and gauge bosons. Across the CD transition, another phase, the electron phase, is realized, which corresponds to the confinement phase of gauge theory. The quasiparticles in this phase are conventional electrons, which may be viewed as bound states of holons and spinons. In this paper, we demonstrate that the two-dimensional t-J model exhibits the phenomenon of CSS below a certain critical temperature TCD{\mathit{T}}_{\mathrm{CD}}TCD​, the CD transition temperature, and calculate TCD{\mathit{T}}_{\mathrm{CD}}TCD​ as a function of hole concentration. The most important contribution to the realization of CSS comes from nonrelativistic gapless excitations via screening of confining potential among holons and spinons. Reflecting upon two kinds of mean fields, i.e., in the normal and super channels, the resulting CSS deconfinement phase of the t-J model is further classified into Coulomb and Higgs phases. By applying the Polyakov-Susskind theory, they are described by the spin-ordered phase of the isotropic and of the anisotropic XY spin model, respectively.
We demonstrate that the configuration interaction (CI) approximation recaptures essential features of the exact (Bethe-ansatz) solution to the one-dimensional (1D) Hubbard model. As such, it provides a valuable route for describing effects that go beyond mean-field theory for strongly correlated electron systems in higher dimensions. The CI method systematically describes fluctuation and quantum tunneling corrections to the Hartree-Fock approximation (HFA). HFA predicts that doping a half-filled Hubbard chain leads to the appearance of charged spin polarons or charged domain-wall solitons in the antiferromagnetic background. The CI method, on the other hand, describes the quantum dynamics of these charged magnetic solitons and quantum tunneling effects between various mean-field configurations. In this paper, we test the accuracy of the CI method against the exact solution of the one-dimensional Hubbard model. We find remarkable agreement between the energy of the mobile charged bosonic domain wall (as given by the CI method) and the exact energy of the doping hole (as given by the Bethe ansatz) for the entire U/tU/tU/t range. The CI method also leads to a clear demonstration of the spin-charge separation in one dimension. Addition of one doping hole to the half-filled antiferromagnetic chain results in the appearance of two different carriers: a charged bosonic domain wall (which carries the charge but no spin) and a neutral spin-1/2 domain wall (which carries the spin but no charge).
Fermionizing the charge sector and bosonizing the spin part in the SU(2) slave-boson theory, we derive an effective-field theory for dynamics of doped holes in the antiferromagnetically correlated spin background, where spin fluctuations are described by an SO(5) Wess-Zumino-Witten (WZW) theory while dynamics of doped holes is characterized by QED3{\text{QED}}_{3}QED3​ with a chemical-potential term. An important feature of our effective-field theory is the coupling term between valence-bond fluctuations and doped holes. Considering that valence-bond fluctuations are deeply related with monopole excitations of staggered U(1) gauge fields in the bosonic field theory for spin fluctuations, we demonstrate that hole dynamics helps deconfinement of bosonic spinons near the quantum critical point of the SO(5) WZW theory. We solve this effective-field theory in the Eliashberg framework and find non-Fermi-liquid physics in thermodynamics and transport, where z=3z=3z=3 criticality with dynamical exponent zzz plays an important role for hole dynamics. We discuss validity of our field theory, applying it to a doped spin chain and comparing it with the slave-fermion framework. Furthermore, we discuss instability of the anomalous metallic phase against superconductivity and density waves of doped holes, resulting from competition between gauge and valence-bond fluctuations.
Quantum Simulation Strongly interacting chains of fermions are predicted to exhibit two types of collective excitations: spinons, which carry only spin, and holons, which carry only charge. These excitations move at different velocities. Signatures of this so-called spin-charge separation have been observed in solid-state systems, but obtaining direct dynamical evidence is tricky. With this goal in mind, Vijayan et al. perturbed a chain of ultracold interacting fermions housed in a one-dimensional optical lattice by removing one of the atoms. This gave rise to two independent excitations, which the researchers identified as spinons and holons using a quantum gas microscope. Science , this issue p. [186][1] [1]: /lookup/doi/10.1126/science.aay2354