arXiv subjects

A. M. Tsvelik

Publications and source records attributed to A. M. Tsvelik.

160 records · Page 9Linked to original sources

arXiv1995

Logarithmic Operators and Hidden Continuous Symmetry in Critical Disordered Models

We study the model of (2 + 1)-dimensional relativistic fermions in a random non-Abelian gauge potential at criticality. The exact solution shows that the operator expansion contains a conserved current - a generator of a continuous symmetry. The presence of this operator changes the operator product expansion and gives rise to logarithmic contributions to the correlation functions at the critical point. We calculate the distribution function of the local density of states in this model and find that it follows the famous log-normal law.

hep-th↗

arXiv1995

Skyrmion Liquid in SU(2)-invariant Quantum Hall Systems

We report on a theory of the Skyrmion states which occur in quantum Hall regime near certain filling factors. It is shown that in the limit of zero Zeeman splitting in a realistic temperature range the Skyrmion plasma is a liquid described by the effective model of massive two-dimensional Dirac fermions.

cond-mat↗

arXiv1995

Superconductivity in a spin liquid - a one dimensional example

We study a one-dimensional model of interacting conduction electrons with a two-fold degenerate band away from half filling. The interaction includes an on-site Coulomb repulsion and Hund's rule coupling. We show that such one-dimensional system has a divergent Cooper pair susceptibility at T = 0, provided the Coulomb interaction $U$ between electrons on the same orbital and the modulus of the Hund's exchange integral $|J|$ are larger than the interorbital Coulomb interaction. It is remarkable that the superconductivity can be achieved for {\it any} sign of $J$. The opening of spectral gaps makes this state stable with respect to direct electron hopping between the orbitals. The scaling dimension of the superconducting order parameter is found to be between 1/4 (small $U$) and 1/2 (large $U$).

cond-mat↗

arXiv1995

Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains

We study a model of two weakly coupled isotropic spin-1/2 Heisenberg chains with an antiferromagnetic coupling along the chains. It is shown that the system always has a spectral gap. For the case of identical chains the model in the continuous limit is equivalent to 4 decoupled noncritical Ising models. For this case we obtain the exact expressions for the asymptotics of spin-spin correlation functions. When the chains have different exchange integrals the spectrum at low energies is well described by the O(3) nonlinear sigma model. We discuss the topological order parameter related to the gap formation and give a detailed description of the dynamical magnetic susceptibility.

cond-mat↗

arXiv1995

Pedestrian Approach to the Two-Channel Kondo Model

We reformulate the two-channel Kondo model to explicitly remove the unscattered charge degrees of freedom. This procedure permits us to move the non-Fermi liquid fixed point to infinite coupling where we can apply a perturbative strong-coupling expansion. The fixed point Hamiltonian involves a three-body Majorana zero mode whose scattering effects give rise to marginal self-energies. The compactified model is the N=3 member of a family of "O(N)" Kondo models that can be solved by semiclassical methods in the large $N$ limit. For odd $N$, {\em fermionic} "Kink" fluctuations about the $N=\infty$ mean-field theory generate a fermionic $N$-body bound-state which asymptotically decouples at low energies. For N=3, our semi-classical methods fully recover the non-Fermi liquid physics of the original two channel model. Using the same methods, we find that the corresponding O(3) Kondo lattice model develops a spin-gap and a gapless band of coherently propagating three-body bound-states. Its strong-coupling limit offers a rather interesting realization of marginal Fermi liquid behavior.

cond-mat↗

arXiv1995

Anisotropic Spin-1/2 Heisenberg Chain with Open Boundary Conditions

We study the exact solution of the XXZ spin-1/2 Heisenberg chain with a boundary magnetic field in the region where the bulk excitations are gapless. It is shown that a bound state is created near the boundary with a total spin $S = 1/2(π/γ- 1)$ where $\cosγ$ is the anisotropy parameter. When $γ< π/2$ this spin remains underscreened giving rise to non-analytic contributions to the free energy. The IR fixed point is this case belongs to the universality class of the underscreened Kondo model. We argue that the same fixed point appears in the boundary sine-Gordon model when the scaling dimension of the boundary term $1/2 < Δ< 1$.

cond-mat↗

arXiv1995

The Toulose limit of the Multi-Channel Kondo model.

We study the Toulouse limit of the multi-channel Kondo model defined as the limit of maximal anisotropy which can be achieved without changing the infrared behaviour of the model. It is shown that when the number of channels exceeds 2, the interactions do not vanish and the Toulouse limit remains a non-trivial field theory. Considerable simplifications take place only for k = 2, where the Bethe ansatz reproduces the results by Emery and Kivelson.

cond-mat↗

arXiv1995

Superconducting Instability in a 1D lattice of Berry Phase Molecules

We study the 1D model of conduction electrons interacting with local vibronic modes. States in the conduction band are two-fold degenerate both in orbital index and spin. It is shown that such 1D system has a strong tendency to superconductivity. The superconducting pairing originates from coupling of two charge density waves; the scaling dimension of the order parameter is close to 1/4.

cond-mat↗

arXiv1995

Existence of Low-Temperature Critical Regime in 1D Luttinger Liquid with a Weak Link

The exact solution of the boundary sine-Gordon model is studied in the region where the scaling dimension of the boundary field $1 < Δ< 1$. It is shown that at $Δ> 2/3$ the infrared fixed point belongs to the universality class of the underscreened anisotropic Kondo model. The boundary contribution to the specific heat scales as $C \sim T^{2Δ^{-1} - 2}$ at small temperatures.

cond-mat↗

arXiv1994

Capacitance and Transport through an Isolated Impurity Center in 1D Luttinger Liquid

We establish the equivalence between the problem of a solitary potential scatterer in a Luttinger liquid of spinless repulsive fermions and an anisotropic Kondo model where the value of the impurity spin id determined by the scaling dimension of the scattering potential. The Bethe ansatz is used to derive non-perturbative expressions for the capacitance and conductance.

cond-mat↗

arXiv1994

An Exactly Solvable Model of Fermions with Disorder

Non-perturbative results are obtained for multipoint correlation functions of the model of (2 + 1)-dimensional relativistic fermions in a random static non-Abelian gauge potential. The results indicate that the replica symmetry remains unbroken. We calculate the diffuson propagator and show that DC-conductivity for this model is finite. ||

cond-mat↗

arXiv1994

One-Dimensional Kondo Lattice at Half Filling: Charge Properties

The model of Kondo chain with $M$-fold degenerate band of conduction electrons of spin 1/2 at half filling interacting with localized spins $S$ is studied. It is shown that due to the instanton effects the spin sector reveals itself in optical conductivity. Namely, the density of the charge current at large wave vector $k \approx π$ is proportional to the density of topological charge of the staggered magnetization. As a consequence, the optical conductivity at $k = π$ would either have a gap equal to three spin gaps (for $|M - 2S| = $(even) when the spin spectrum is gapful), or show a psedogap $σ(ω, k = π) \sim ω^2$ for $|M - 2S|$ = (odd).

cond-mat↗

arXiv1994

Disorder Effects in Two-Dimensional d-wave Superconductors

Influence of weak nonmagnetic impurities on the single-particle density of states $ρ(ω)$ of two-dimensional electron systems with a conical spectrum is studied. We use a nonperturbative approach, based on replica trick with subsequent mapping of the effective action onto a one-dimensional model of interacting fermions, the latter being treated by Abelian and non-Abelian bosonization methods. It is shown that, in a d-wave superconductor, the density of states, averaged over randomness, follows a nontrivial power-law behavior near the Fermi energy: $ρ(ω) \sim |ω|^α$. The exponent $α>0$ is calculated for several types of disorder. We demonstrate that the property $ρ(0) = 0$ is a direct consequence of a {\it continuous} symmetry of the effective fermionic model, whose breakdown is forbidden in two dimensions. As a counter example, we consider another model with a conical spectrum - a two-dimensional orbital antiferromagnet, where static disorder leads to a finite $ρ(0)$ due to breakdown of a {\it discrete} (particle-hole) symmetry.

cond-mat↗

arXiv1993

Semiclassical Solution of One Dimensional Model of Kondo Insulator

The model of Kondo chain with $M$-fold degenerate band of conduction electrons of spin 1/2 interacting with localized spins $S$ is studied for the case when the electronic band is half filled. It is shown that the spectrum of spin excitations in the continuous limit is described by the O(3) nonlinear sigma model with the topological term with $θ= π(2S - M)$. For a case $|M - 2S| = $(even) the system is an insulator and single electron excitations at low energies are massive spin polarons. Otherwise the density of states has a pseudogap and vanishes only at the Fermi level. The relevance of this picture to higher dimensional Kondo insulators is discussed.

cond-mat↗

arXiv1992

Low-Temperature Thermodynamics of $A^{(2)}_2$ and su(3)-invariant Spin Chains

We formulate the thermodynamic Bethe Ansatz (TBA) equations for the closed (periodic boundary conditions) $A^{(2)}_2$ quantum spin chain in an external magnetic field, in the (noncritical) regime where the anisotropy parameter $η$ is real. In the limit $η\to 0$, we recover the TBA equations of the antiferromagnetic su(3)-invariant chain in the fundamental representation. We solve these equations for low temperature and small field, and calculate the specific heat and magnetic susceptibility.

hep-th↗

arXiv1992

New Fermionic Description of Quantum S = 1/2 Antiferromargnet

A novel approach to S =1/2 antiferromagnets with strong fluctuations based on the representation of spin-1/2 operators as bylinear forms of real (Majorana) fermions is suggested. This representation has the advantage of being irreducible without any constraints on the fermionic Hilbert space. This property allows to derive an effective Hamiltonian for low-lying excitations in the spin liquid state. It is proven that these excitations are S = 1 real fermions.

cond-mat↗