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André LeClair

Publications and source records attributed to André LeClair.

47 records · Page 3Linked to original sources
arXiv2008

A model of a 2d non-Fermi liquid with SO(5) symmetry, AF order, and a d-wave SC gap

Demanding a consistent quantum field theory description of spin 1/2 particles near a circular Fermi surface in 2d leads to a unique fermionic theory with relevant quartic interactions which has an emergent Lorentz symmetry and automatically has an Sp(4) = SO(5) internal symmetry. The free theory has resistivity linear in temperature. The interacting theory has a low-energy interacting fixed point and is thus a non-Landau/Fermi liquid. Anti-ferromagnetic (AF) and superconducting (SC) order parameters are bilinears in the fields and form the 5-dimensional vector representation of SO(5). An AF phase occurs at low doping which terminates in a first order transition. We incorporate momentum dependent scattering of Cooper pairs near the Fermi surface to 1-loop and derive a new kind of SC gap equation beyond mean field with a d-wave gap solution. Taking into account the renormalization group (RG) scaling properties near the low energy fixed point, we calculate the complete phase diagram as a function of doping, which shows some universal geometric features. The d-wave SC dome terminates on the over-doped side at the fixed point of the RG,which is a quantum critical point. Optimal doping is estimated to occur just below 3/2π^2. The critical temperature for SC at optimal doping is set mainly by the universal nodal Fermi velocity and lattice spacing, and is estimated to average around 140K for LSCO. The pseudogap energy scale is identified as the RG scale of the coupling.

cond-mat.str-el↗
arXiv2008

Super Spin-Charge Separation for class A, C, and D disorder

We prove versions of super spin-charge separation for all three of the symmetry groups SU(N), Sp(2N), and SO(N) of disordered Dirac fermions in 2+1 dimensions, which involve the supercurrent-algebras gl (1|1)_{N}, osp(2|2)_{-2N}, and osp(2|2)_N respectively. For certain restricted classes of disordered potentials, the latter supercurrent algebra based conformal field theories can arise as non-trivial low energy fixed points. For all cases with such a fixed point, we compute the density of states exponents as a function of N.

math-ph↗
arXiv2008

Critical points of 2d disordered Dirac fermions: the Quantum Hall Transitions revisited

We propose a resolution of the renormalization group flow for the disordered Dirac fermion theories describing the quantum Hall transition (QHT) and spin Quantum Hall transition (SQHT), which previously revealed no perturbative fixed points at 1-loop and higher. The approach involves carrying out the flow in 2 stages, the first stage utilizing a new form of super spin-charge separation to flow to gl(1|1)_N and osp(2|2)_{-2N} supercurrent algebra theories, where N is the number of copies. This leads to the unconventional feature that at the critical point the exponents depend on the original number of copies N. In the second stage, additional forms of disorder are incorporated as dimension zero logarithmic operators, and the resulting actions have explicit forms in terms of two scalar fields and a symplectic fermion. Under some assumptions, the multi-fractal exponents are computed with the result q(1-q)/4 and q(1-q)/8 for the QHT and SQHT respectively, and are within a few percent of numerical estimates.

cond-mat.mes-hall↗
arXiv2008

A unique non-Landau/Fermi liquid in 2d for high Tc superconductivity

It is shown that the main features of the phase diagram for high Tc superconductivity can be calculated as a function of doping in a simple, essentially unique non-Landau/Fermi liquid with quartic interactions. The phase diagram depends on a single parameter 0<gamma<1 determined by the strength of the interaction at short distances. A new d-wave gap equation has solutions that fall under a superconducting dome, which terminates at the renormalization group fixed point. Optimal doping is estimated to occur just below 3/2 π^2. The overall scale for Tc is set by the recently measured universal nodal Fermi velocity and lattice spacing, and is estimated to be 120K < Tc < 160K for LaSrCuO.

cond-mat.str-el↗
arXiv2007

The gl(1|1) super-current algebra: the role of twist and logarithmic fields

A free field representation of the gl(1|1)_k current algebra at arbitrary level k is given in terms of two scalar fields and a symplectic fermion. The primary fields for all representations are explicitly constructed using the twist and logarithmic fields in the symplectic fermion sector. A closed operator algebra is described at integer level k. Using a new super spin charge separation involving gl(1|1)_N and su(N)_0, we describe how the gl(1|1)_N current algebra can describe a non-trivial critical point of disordered Dirac fermions. Local gl(1|1) invariant lagrangians are defined which generalize the Liouville and sine-Gordon theories. We apply these new tools to the spin quantum Hall transition and show that it can be described as a logarithmic perturbation of the osp(2|2)_k current algebra at k=-2.

hep-th↗
arXiv2007

Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models

We study a model of N-component complex fermions with a kinetic term that is second order in derivatives. This symplectic fermion model has an Sp(2N) symmetry, which for any N contains an SO(3) subgroup that can be identified with rotational spin of spin-1/2 particles. Since the spin-1/2 representation is not promoted to a representation of the Lorentz group, the model is not fully Lorentz invariant, although it has a relativistic dispersion relation. The hamiltonian is pseudo-hermitian, H^\dagger = C H C, which implies it has a unitary time evolution. Renormalization-group analysis shows the model has a low-energy fixed point that is a fermionic version of the Wilson-Fisher fixed points. The critical exponents are computed to two-loop order. Possible applications to condensed matter physics in 3 space-time dimensions are discussed.

hep-th↗
arXiv2007

Interacting Bose and Fermi gases in low dimensions and the Riemann hypothesis

We apply the S-matrix based finite temperature formalism to non-relativistic Bose and Fermi gases in 1+1 and 2+1 dimensions. In the 2+1 dimensional case, the free energy is given in terms of Roger's dilogarithm in a way analagous to the relativistic 1+1 dimensional case. The 1d fermionic case with a quasi-periodic 2-body potential provides a physical framework for understanding the Riemann hypothesis.

math-ph↗
arXiv2007

Quantum critical spin liquids and conformal field theory in 2+1 dimensions

We describe new conformal field theories based on symplectic fermions that can be extrapolated between 2 and 4 dimensions. The critical exponents depend continuously on the number of components N of the fermions and the dimension D. In the context of anti-ferromagnetism, the N=2 theory is proposed to describe a deconfined quantum critical spin liquid corresponding to a transition between a Neel ordered phase and a VBS-like phase.

cond-mat.str-el↗
arXiv2006

Quantum critical spin liquids and superconductivity in the cuprates

We describe a new kind of quantum critical point in the context of quantum anti-ferromagnetism in 2d that can be understood as a quantum critical spin liquid. Based on the comparison of exponents with previous numerical work, we argue it describes a transition from an anti-ferromagnetic Néel ordered state to a VBS-like state. We argue further that the symplectic fermions capture the proper degrees of freedom in the zero temperature phase that is the parent to the superconducting phase in the cuprates. We then show that our model reproduces some features found recently in experiments and also in the Hubbard model.

cond-mat.str-el↗
arXiv2006

Quantum statistical mechanics of gases in terms of dynamical filling fractions and scattering amplitudes

We develop a finite temperature field theory formalism in any dimension that has the filling fractions as the basic dynamical variables. The formalism efficiently decouples zero temperature dynamics from the quantum statistical sums. The zero temperature `data' is the scattering amplitudes. A saddle point condition leads to an integral equation which is similar in spirit to the thermodynamic Bethe ansatz for integrable models, and effectively resums infinite classes of diagrams. We present both relativistic and non-relativistic versions.

hep-th↗