We consider solutions of the matrix KP hierarchy that are elliptic functions of the first hierarchical time $t_1=x$. It is known that poles $x_i$ and matrix residues at the poles $rho_i^{alpha beta}=a_i^{alpha}b_i^{beta}$ of such solutions as functio
ns of the time $t_2$ move as particles of spin generalization of the elliptic Calogero-Moser model (elliptic Gibbons-Hermsen model). In this paper we establish the correspondence with the spin elliptic Calogero-Moser model for the whole matrix KP hierarchy. Namely, we show that the dynamics of poles and matrix residues of the solutions with respect to the $k$-th hierarchical time of the matrix KP hierarchy is Hamiltonian with the Hamiltonian $H_k$ obtained via an expansion of the spectral curve near the marked points. The Hamiltonians are identified with the Hamiltonians of the elliptic spin Calogero-Moser system with coordinates $x_i$ and spin degrees of freedom $a_i^{alpha}, , b_i^{beta}$.
We consider solutions of the 2D Toda lattice hierarchy which are elliptic functions of the zeroth time t_0=x. It is known that their poles as functions of t_1 move as particles of the elliptic Ruijsenaars-Schneider model. The goal of this paper is to
extend this correspondence to the level of hierarchies. We show that the Hamiltonians which govern the dynamics of poles with respect to the m-th hierarchical times t_m and bar t_m of the 2D Toda lattice hierarchy are obtained from expansion of the spectral curve for the Lax matrix of the Ruijsenaars-Schneider model at the marked points.
We consider solutions of the KP hierarchy which are elliptic functions of $x=t_1$. It is known that their poles as functions of $t_2$ move as particles of the elliptic Calogero-Moser model. We extend this correspondence to the level of hierarchies an
d find the Hamiltonian $H_k$ of the elliptic Calogero-Moser model which governs the dynamics of poles with respect to the $k$-th hierarchical time. The Hamiltonians $H_k$ are obtained as coefficients of the expansion of the spectral curve near the marked point in which the Baker-Akhiezer function has essential singularity.
We consider solutions of the matrix KP hierarchy that are trigonometric functions of the first hierarchical time $t_1=x$ and establish the correspondence with the spin generalization of the trigonometric Calogero-Moser system on the level of hierarch
ies. Namely, the evolution of poles $x_i$ and matrix residues at the poles $a_i^{alpha}b_i^{beta}$ of the solutions with respect to the $k$-th hierarchical time of the matrix KP hierarchy is shown to be given by the Hamiltonian flow with the Hamiltonian which is a linear combination of the first $k$ higher Hamiltonians of the spin trigonometric Calogero-Moser system with coordinates $x_i$ and with spin degrees of freedom $a_i^{alpha}, , b_i^{beta}$. By considering evolution of poles according to the discrete time matrix KP hierarchy we also introduce the integrable discrete time version of the trigonometric spin Calogero-Moser system.
We develop a formalism to study the Resonant Inelastic X-ray Scattering (RIXS) response in metals based on the diagrammatic expansion for its cross section. The standard approach to the solution of the RIXS problem relies on two key approximations: s
hort-range potentials and non-interacting conduction electrons. However, these approximations are inaccurate for charged particles in metals, where the long-range Coulomb interaction and dynamic screening effects are very important. In this work we study how to extract important information about collective excitations in the Coulomb plasma, plasmons and electron-hole pairs, from RIXS data. We find that single- and multi-plasmon excitations can easily be distinguished by positions of the corresponding peaks, singularities, and their intensities. We also discuss the hybrid processes, where plasmon emission is accompanied by excitation of electron-hole pairs, and study how they manifest themselves.
In a number of physical situations, from polarons to Dirac liquids and to non-Fermi liquids, one encounters the beyond quasiparticles regime, in which the inelastic scattering rate exceeds the thermal energy of quasiparticles. Transport in this regim
e cannot be described by the kinetic equation. We employ the Diagrammatic Monte Carlo method to study the mobility of a Fr{o}hlich polaron in this regime and discover a number of non-perturbative effects: a strong violation of the Mott-Ioffe-Regel criterion at intermediate and strong couplings, a mobility minimum at $T sim Omega$ in the strong-coupling limit ($Omega$ is the optical mode frequency), a substantial delay in the onset of an exponential dependence of the mobility for $T<Omega$ at intermediate coupling, and complete smearing of the Drude peak at strong coupling. These effects should be taken into account when interpreting mobility data in materials with strong electron-phonon coupling.
We introduce the method of stochastic lists to deal with a multi-variable positive function, defined by a self-consistent equation, typical for certain problems in physics and mathematics. In this approach, the functions properties are represented st
atistically by lists containing a large collection of sets of coordinates (or walkers) that are distributed according to the functions value. The coordinates are generated stochastically by the Metropolis algorithm and may replace older entries according to some protocol. While stochastic lists offer a solution to the impossibility of efficiently computing and storing multi-variable functions without a systematic bias, extrapolation in the inverse of the number of walkers is usually difficult, even though in practice very good results are found already for short lists. This situation is reminiscent of diffusion Monte Carlo, and is hence generic for all population-based methods. We illustrate the method by computing the lowest-order vertex corrections in Hedins scheme for the Frohlich polaron and the ground state energy and wavefunction of the Heisenberg model in two dimensions.
The repulsive Fermi Hubbard model on the square lattice has a rich phase diagram near half-filling (corresponding to the particle density per lattice site $n=1$): for $n=1$ the ground state is an antiferromagnetic insulator, at $0.6 < n lesssim 0.8$,
it is a $d_{x^2-y^2}$-wave superfluid (at least for moderately strong interactions $U lesssim 4t$ in terms of the hopping $t$), and the region $1-n ll 1$ is most likely subject to phase separation. Much of this physics is preempted at finite temperatures and to an extent driven by strong magnetic fluctuations, their quantitative characteristics and how they change with the doping level being much less understood. Experiments on ultra-cold atoms have recently gained access to this interesting fluctuation regime, which is now under extensive investigation. In this work we employ a self-consistent skeleton diagrammatic approach to quantify the characteristic temperature scale $T_{M}(n)$ for the onset of magnetic fluctuations with a large correlation length and identify their nature. Our results suggest that the strongest fluctuations---and hence highest $T_{M}$ and easiest experimental access to this regime---are observed at $U/t approx 4-6$.
Applying Feynman diagrammatics to non-fermionic strongly correlated models with local constraints might seem generically impossible for two separate reasons: (i) the necessity to have a Gaussian (non-interacting) limit on top of which the perturbativ
e diagrammatic expansion is generated by Wicks theorem, and (ii) the Dysons collapse argument implying that the expansion in powers of coupling constant is divergent. We show that for arbitrary classical lattice models both problems can be solved/circumvented by reformulating the high-temperature expansion (more generally, any discrete representation of the model) in terms of Grassmann integrals. Discrete variables residing on either links, plaquettes, or sites of the lattice are associated with the Grassmann variables in such a way that the partition function (and correlations) of the original system and its Grassmann-field counterpart are identical. The expansion of the latter around its Gaussian point generates Feynman diagrams. A proof-of-principle implementation is presented for the classical 2D Ising model. Our work paves the way for studying lattice gauge theories by treating bosonic and fermionic degrees of freedom on equal footing.
We present a controlled rare-weak-link theory of the superfluid-to-Bose/Mott glass transition in one-dimensional disordered systems. The transition has Kosterlitz-Thouless critical properties but may occur at an arbitrary large value of the Luttinger
parameter $K$. In contrast to the scenario by Altman {it et al.} [Phys. Rev. B {bf 81}, 174528 (2010)], the hydrodynamic description is valid under the correlation radius and defines criticality via the renormalization of microscopically weak links, along the lines of Kane and Fisher [Phys. Rev. Lett. {bf 68}, 1220 (1992)]. The hallmark of the theory is the relation $K^{(c)}=1/zeta$ between the critical value of the Luttinger parameter at macroscopic scales and the microscopic (irrenormalizable) exponent $zeta$ describing the scaling $propto 1/N^{1-zeta}$ for the strength of the weakest link among the $N/L gg 1$ disorder realizations in a system of fixed mesoscopic size $L$.
