Yusuke Nishida

Nonrelativistic conformal field theories

We study representations of the Schrodinger algebra in terms of operators in nonrelativistic conformal field theories. We prove a correspondence between primary operators and eigenstates of few-body systems in a harmonic potential. Using the correspondence we compute analytically the energy of fermions at unitarity in a harmonic potential near two and four spatial dimensions. We also compute the energy of anyons in a harmonic potential near the bosonic and fermionic limits.

ϵ Expansion for a Fermi Gas at Infinite Scattering Length

We show that there exists a systematic expansion around four spatial dimensions for Fermi gas in the unitarity regime. We perform the calculations to leading and next-to-leading orders in the expansion over E = 4-d, where d is the dimensionality of space. We find the ratio of chemical potential and Fermi energy to be mu/epsilon(F) =1/2 (E 3/2) + 1/16 (E 5/2) lnE -0.0246E (5/2) + ... and the ratio of the gap in the fermion quasiparticle spectrum and the chemical potential to be Delta/mu =2E(-1) - 0.691 + ... . The minimum of the fermion dispersion curve is located at |p|=(2mepsilon(0))(1/2), where epsilon_(0)/mu=2+O(E). Extrapolation to d=3 gives results consistent with Monte Carlo simulations.

Phase structures of strong coupling lattice QCD with finite baryon and isospin density

Quantum chromodynamics (QCD) at finite temperature (T), baryon chemical potential (muB) and isospin chemical potential (muI) is studied in the strong coupling limit on a lattice with staggered fermions. With the use of large dimensional expansion and the mean field approximation, we derive an effective action written in terms of the chiral condensate and pion condensate as a function of T, muB and muI. The phase structure in the space of T and muB is elucidated, and simple analytical formulas for the critical line of the chiral phase transition and the tricritical point are derived. The effects of a finite quark mass (m) and finite muI on the phase diagram are discussed. We also investigate the phase structure in the space of T, muI and m, and clarify the correspondence between color SU(3) QCD with finite isospin density and color SU(2) QCD with finite baryon density. Comparisons of our results with those from recent Monte Carlo lattice simulations on finite density QCD are given.

BCS-BEC crossover in a relativistic superfluid and its significance to quark matter

The character change of a superfluid state due to the variation of the attractive force is investigated in the relativistic framework with a massive fermion. Two crossovers are found. One is a crossover from the usual BCS state to the Bose-Einstein condensation (BEC) of bound fermion pairs. The other is from the BEC to the relativistic Bose-Einstein condensation (RBEC) of nearly massless bound pairs where antiparticles as well as particles dominate the thermodynamics. Possible realization of the BEC and RBEC states in the quark matter is also pointed out.

Fermi gas near unitarity around four and two spatial dimensions

We construct systematic expansions around four and two spatial dimensions for a Fermi gas near the unitarity limit. Near four spatial dimensions such a Fermi gas can be understood as a weakly interacting system of fermionic and bosonic degrees of freedom. To the leading and next-to-leading orders in the expansion over {epsilon}=4-d, with d being the dimensionality of space, we calculate the thermodynamic quantities and the fermion quasiparticle spectrum, both at unitarity and around the unitarity point. Then the phase structure of the polarized Fermi gas in the unitary regime is studied in the {epsilon} expansion. At unitarity the unpolarized superfluid state and a fully polarized normal state are separated by a first order phase transition. However, on the BEC side of the unitarity point, in a certain range of the two-body binding energy, these two phases are separated in the phase diagram by more exotic phases, including gapless superfluid phases with one or two Fermi surfaces and a superfluid phase with a spatially varying condensate. We also show that the unitary Fermi gas near two spatial dimensions is weakly interacting, and calculate the thermodynamic quantities and the fermion quasiparticle spectrum in the expansion over {epsilon}=d-2.

Universal Fermi Gas with Two-and Three-Body Resonances

We consider a Fermi gas with two components of different masses, with the s-wave two-body interaction tuned to unitarity. In the range of mass ratio 8.62<M/m<13.6, it is possible for a short-range interaction between heavy fermions to produce a resonance in a three-body channel. The resulting system is scale invariant and has universal properties, and is very strongly interacting. When M/m is slightly above the lower limit 8.62, the ground state energy of a 2ratio1 mixture of heavy and light fermions is less than 2% of the energy of a noninteracting gas with the same number densities. We derive exact relationships between the pressures of the unitary Fermi gases with and without three-body resonance when the mass ratio is close to the critical values of 8.62 and 13.6.

Thermodynamics of strong coupling 2-color QCD with chiral and diquark condensates

Abstract Two-color quantum chromodynamics (QCD with Nc=2) at finite temperature T and chemical potential μ is revisited in the strong coupling limit on the lattice with staggered fermions. The phase structure in the space of T, μ, and the quark mass m is elucidated with the use of the mean field approximation and the 1/d expansion (d being the number of spatial dimensions). We put special emphasis on the interplay among the chiral condensate 〈 q q〉 , the diquark condensate 〈qq〉, and the quark density 〈q † q〉 in the T-μ-m space. Simple analytic formulae are also derived without assuming μ nor m being small. Qualitative comparisons are made between our results and those of recent Monte-Carlo simulations in 2-color QCD.

Unitary Fermi gas at finite temperature in the {epsilon} expansion

Thermodynamics of the unitary Fermi gas at finite temperature is investigated from the perspective of the expansion over {epsilon}=4-d with d being the dimensionality of space. We show that the thermodynamics is dominated by bosonic excitations in the low temperature region T<<T{sub c}. Analytic formulas for the thermodynamic functions as functions of the temperature are derived to the lowest order in {epsilon} in this region. In the high temperature region where T{approx}T{sub c}, bosonic and fermionic quasiparticles are excited. We determine the critical temperature T{sub c} of the superfluid phase transition and the thermodynamic functions around T{sub c} to the leading and next-to-leading orders in {epsilon}.

Induced p-wave superfluidity in two dimensions : Brane world in cold atoms and nonrelativistic defect CFTs

Abstract We propose to use a two-species Fermi gas with the interspecies s-wave Feshbach resonance to realize p-wave superfluidity in two dimensions. By confining one species of fermions in a two-dimensional plane immersed in the background three-dimensional Fermi sea of the other species, an attractive interaction is induced between two-dimensional fermions. We compute the pairing gap in the weak-coupling regime and show that it has the symmetry of p x + ip y . Because the magnitude of the pairing gap increases toward the unitarity limit, it is possible that the critical temperature for the p x + ip y -wave superfluidity becomes within experimental reach. The resulting system has a potential application to topological quantum computation using vortices with non-Abelian statistics. We also discuss aspects of our system in the unitarity limit as a “nonrelativistic defect conformal field theory (CFT)”. The reduced Schrodinger algebra, operator-state correspondence, scaling dimensions of composite operators, and operator product expansions are investigated.

Renormalization group analysis of resonantly interacting anyons

We formulate a field theory for resonantly interacting anyons, that enables us to perform a perturbative calculation near the fermionic limit. We derive renormalization group equations for three-body and four-body couplings at one-loop order. In addition to two fixed points, we find a limit cycle behavior in the four-body coupling, which implies an infinite set of bound states in the four-anyon system.