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A new analytic treatment of the two-dimensional Hubbard model at finite temperature and chemical potential is presented. A next nearest neighbor hopping term of strength t' is included. This analysis is based upon a formulation of the…
Motivated by recent findings due to Wiegmann and Zabrodin, Faddeev and Kashaev concerning the appearence of the quantum U_q(sl(2)) symmetry in the problem of a Bloch electron on a two-dimensional magnetic lattice, we introduce a…
We have simulated the two-dimensional $RP^2$ and $RP^3$ $\sigma$-models, at correlation lengths up to about 220 (resp.\ 30), using a Wolff-type embedding algorithm. We see no evidence of asymptotic scaling. Indeed, the data rule out the…
Gauge theories embedded into higher-dimensional spaces with certain topologies acquire inductance terms, which reflect the energy cost of topological charges accumulated in the extra dimensions. We compute topological susceptibility in the…
Hopf insulator is a representative class of three-dimensional topological insulators beyond the standard topological classification methods based on K-theory. In this letter, we discover the metallic counterpart of the Hopf insulator in the…
Local symmetries is one of the most successful themes in modern theoretical physics. Although they are usually associated to Lie algebras, a gradual increase of interest in more general situations where local symmetries are associated to…
In this paper, we study topological properties of 3D lattice dimer model. We demonstrate, that the dimer model on a bipartite lattice possesses topological defects, which are exactly characterized by Hopf invariant. We derive its explicit…
In arXiv:0902.4032 [hep-th] an O(D,D)-covariant sigma model describing the embedding of a closed world-sheet into the 2D-dimensional twisted torus was proposed. Such sigma models provide a universal description of string theory with target…
A three-dimensional effective theory of the finite-temperature SU(5)+adjoint Higgs model is constructed using the method of dimensional reduction. The resulting theory can be used for computer simulations of the GUT phase transition of the…
Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We…
Establishing the fundamental relation between the homotopy invariants and the band topology of Hamiltonians has played a critical role in the recent development of topological phase research. In this work, we establish the homotopy…
We consider the $\mathcal{N}=2$ SYM theory with gauge group SU($N$) and a matter content consisting of one multiplet in the symmetric and one in the anti-symmetric representation. This conformal theory admits a large-$N$ 't Hooft expansion…
We consider a two-dimensional $\sigma$-model with discrete icosahedral/dodecahedral symmetry. Using the perturbative renormalization group, we argue that this model has a different continuum limit with respect to the O(3) $\sigma$ model.…
We have experimentally realized novel space-time inversion (P-T) invariant Z2-type topological semimetal-bands, via an analogy between the momentum space and a controllable parameter space in superconducting quantum circuits. By measuring…
The 3D vector van der Waals (or conformal) nonlinear sigma-model is proposed. It is shown that it has the "hedgehog"-like topological excitations with logarithmic energy. Their "neutral" configurations have nontrivial topological structures…
This thesis is based on the publications arXiv:1106.4253, arXiv:1206.2920, arXiv:1210.2590. We construct warped "AdS_4 x S^2 x S^2 x \Sigma" type IIB supergravity solutions dual to the infrared fixed points of all 3d N=4 linear and circular…
We analyse super non-Abelian T-duality for principal chiral models, symmetric space sigma models, and semi-symmetric space sigma models for general Lie supergroups. This includes T-duality along both bosonic and fermionic directions. As an…
Expanding Nambu-Goto action near infinitely long string vacuum one can compute scattering amplitudes of 2d massless fields representing transverse string coordinates. As was shown in arXiv:1203.1054, the resulting S-matrix is integrable, in…
We propose a two-dimensional (2D) version of Thouless pumping that can be realized by using ultracold atoms in optical lattices. To be specific, we consider a 2D square lattice tight-binding model with an obliquely introduced superlattice.…
We elaborate on the dynamics of noncommutative two-dimensional gauge field theories. We consider U(N) gauge theories with fermions in either the fundamental or the adjoint representation. Noncommutativity leads to a rather non-trivial…