Related papers: Universality relations in non-solvable quantum spi…
Using conformal perturbation theory, we show that for some classes of the one-dimensional quantum liquids that possess the Luttinger liquid fixed point in the low energy limit, the Drude weight at finite temperatures is non-vanishing, even…
Uncertainty relations are shown to have nothing specific for quantum mechanics, being the general property valid for arbitrary function. A wave function of a particle having precisely defined position and momentum in QM simultaneously is…
Rarely noted paradoxes and their resolution lead to non-Hermitian behaviors due to boundary terms, even for closed systems and with real potentials. The role played by these non-Hermiticities on quantum mechanical uncertainty relations is…
We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…
Interacting quantum many-body systems constitute a fascinating playground for researchers since they form quantum liquids with correlated ground states and low-lying excitations, which exhibit universal behaviour. In fermionic systems, such…
We consider the non-analytic temperature dependences of the specific heat coefficient, C(T)/T, and spin susceptibility, \chi_{s} (T), of 2D interacting fermions beyond the weak-coupling limit. We demonstrate within the Luttinger-Ward…
We review the correspondence between strongly coupled lattice multiflavor Schwinger models and SU(N) antiferromagnetic chains. We show that finding the low lying states of the gauge models is equivalent to solving an SU(N) Heisenberg…
Quantum loop and dimer models are archetypal examples of correlated systems with local constraints. Obtaining generic solutions for these models is difficult due to the lack of controlled methods to solve them in the thermodynamic limit.…
It is shown that Wen's effective theory correctly describes the Tomonaga-Luttinger liquid at the edge of a system of non-interacting composite fermions. However, the weak residual interaction between composite fermions appears to be a…
In this paper, we seek to prove the equality of the $q$-graded fermionic sums conjectured by Hatayama et al. in its full generality, by extending the results of Di Francesco and Kedem to the non-simply laced case. To this end, we will…
We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants ${\rm det}(1+\hat{A}\hat{B})$, where $A(\epsilon)$ and $B(t)$ have…
We generalized the Fermi liquid theory to N component systems with SU(N) symmetry. We emphasize the important role of fluctuations when N is large. These fluctuations dramatically modifies the properties for repulsive Fermi gases, in…
We develop a systematic effective field theory of hydrodynamics for many-body systems on the lattice with global continuous non-Abelian symmetries. Models with continuous non-Abelian symmetries are ubiquitous in physics, arising in diverse…
We demonstrate that the notion of spin-charge separation as follows from the Tomonaga-Luttinger theory of relativistic fermions does not suffice to completely specify the Luttinger liquid state associated with the fermions of condensed…
We review recent advances in experimental and theoretical understanding of spin transport in strongly interacting Fermi gases. The central new phenomenon is the observation of a lower bound on the (bare) spin diffusivity in the strongly…
We consider zero temperature behavior of dynamic response functions of 1D systems near edges of support in momentum-energy plane $(k, \omega).$ The description of the singularities of dynamic response functions near an edge $\epsilon(k)$ is…
In this comment we show that the experimental results for a universally valid uncertainty relation in ref.[J. Erhart et al. Nat. Phys.(2012)10.1038/nphys2194]cannot be justified. The experiments cannot be recognized to establish a violation…
Luttinger liquid theory accounts for the low energy boson excitations of one-dimensional quantum liquids, but disregards the high energy excitations. The most important high energy excitations are holes which have infinite lifetime at zero…
We develop an operator-based approach to the problem of Luttinger liquid conductor in a non-equilibrium stationary state. We show that the coherent-state many-body fermionic density matrix as well as all fermionic correlation functions out…
The behavior of fermions with two spin states that interact with a large scattering length is constrained by universal relations that hold for any state of the system. These relations involve a central property of the system called the…