Gennady Y. Chitov

First temperature corrections to the Fermi-liquid fixed point in two dimensions

We calculate using perturbative calculations and Ward identities the basic parameters of the Fermi Liquid: the scattering vertex, the Landau interaction function, the effective mass, specific heat, and physical susceptibilities for a model of two-dimensional (2D) fermions with a short ranged interaction at non-zero temperature. The leading temperature dependence of the spin components of the scattering vertex, the Landau function, and the spin susceptibility is found to be linear. We find that the standard T=0 relationships for a Galilean-invariant Fermi Liquid are violated by finite-temperature terms. The coefficients in the temperature corrections to these relationships involve a subtle interplay between contributions from small and large (

Quantum criticality in dimerized spin ladders

\sim 2k_F

Numerical study of critical properties and hidden orders in dimerized spin ladders

) momentum processes. A connection with previous studies of the 2D Fermi-Liquid parameters is discussed. We conclude that the linear leading temperature dependence of the parameters is a generic feature of the 2D Fermi Liquid.

Spin-Peierls instability in the spin- 1 ∕ 2 Heisenberg three-leg ladder

We analyze a possibility of quantum criticality (gaplessness) in dimerized antiferromagnetic two- and three-leg spin-1/2 ladders. Contrary to earlier studies of these models, we examine different dimerization patterns in the ladder. We find that ladders with the columnar dimerization order have lower zero-temperature energies and they are always gapped. For the staggered dimerization order, we find the quantum critical lines, in agreement with earlier analyses. The bond mean-field theory we apply, demonstrates its quantitative accuracy and agrees with available numerical results. We conclude that unless some mechanism for locking dimerization into the energetically less favorable staggered configuration is provided, the dimerized ladders do not order into the phase where the quantum criticality occurs.

FERMI LIQUID AS A RENORMALIZATION-GROUP FIXED POINT : THE ROLE OF INTERFERENCE IN THE LANDAU CHANNEL

Dimerized antiferromagnetic spin- 1 ladders are known to exhibit a quantum critical phase transition in the ground state, the existence or absence of which is dependent on the dimerization pattern of the ladder. The gapped phases cannot be distinguished by the conventional Landau long-range order parameter. However, they possess a non-local (hidden) string order parameter, which is nonzero in one phase and vanishes in the other. We use an exact diagonalization technique to calculate ground state energies, energy gaps and string order parameters of dimerized two- and three-leg Heisenberg ladders, as well as a critical scaling analysis to yield estimates of the critical exponents � and �.

Renormalization-group approach to Fermi-liquid theory

Department of Physics, Laurentian University, Ramsey Lake Road, Sudbury, ON, P3E 2C6, Canada(Dated: February 1, 2008)Because the three-leg ladder behaves like a renormalized single Heisenberg chain we argue that aspin-Peierls instability must occur in this system when it is coupled to three-dimensional phonons.Using the bond-mean-field theory, we show that this is indeed the case. The dimerized state belowthe spin-Peierls transition temperature forms into the columnar dimerized phase not the staggeredone. This contrasts with the argument based on antiferromagnetism. A physical argument basedrather on spin bonding into singlets explains why the columnar configuration is favored. No quantumcriticality (gaplessness) can occur in the columnar arrangement of the dimerized chains.

RENORMALIZATION-GROUP STUDY OF INTERACTING ELECTRONS

We apply the finite-temperature renormalization-group (RG) to a model based on an effective action with a short-range repulsive interaction and a rotation invariant Fermi surface. The basic quantities of Fermi liquid theory, the Landau function and the scattering vertex, are calculated as fixed points of the RG flow in terms of the effective actions interaction function. The classic derivations of Fermi liquid theory, which apply the Bethe-Salpeter equation and amount to summing direct particle-hole ladder diagrams, neglect the zero-angle singularity in the exchange particle-hole loop. As a consequence, the antisymmetry of the forward scattering vertex is not guaranteed and the amplitude sum rule must be imposed by hand on the components of the Landau function. We show that the strong interference of the direct and exchange processes of particle-hole scattering near zero angle invalidates the ladder approximation in this region, resulting in temperature-dependent narrow-angle anomalies in the Landau function and scattering vertex. In this RG approach the Pauli principle is automatically satisfied. The consequences of the RG corrections on Fermi liquid theory are discussed. In particular, we show that the amplitude sum rule is not valid.

Ordering in two-dimensional Ising models with competing interactions

We show that the renormalization-group (RG) approach to interacting fermions at one-loop order recovers Fermi-liquid-theory results when the forward scattering zero sound and exchange channels are both taken into account. The Landau parameters are related to the fixed point value of the {Omega} limit of the forward scattering vertex. We specify the conditions under which the results obtained at one-loop order hold at all orders in a loop expansion. We also emphasize the similarities between our RG approach and the diagrammatic derivation of Fermi-liquid theory. {copyright} {ital 1996 The American Physical Society.}

On the stacking charge order in NaV2O5

The renormalization-group (RG) approach proposed earlier by Shankar for interacting spinless fermions at

Infinite cascades of phase transitions in the classical Ising chain

T=0