46 research outputs found
Infinite Matrix Product States for long range SU(N) spin models
We construct 1D and 2D long-range SU(N) spin models as parent Hamiltonians
associated with infinite matrix product states. The latter are constructed from
correlators of primary fields in the SU(N) level 1 WZW model. Since the
resulting groundstates are of Gutzwiller-Jastrow type, our models can be
regarded as lattice discretizations of fractional quantum Hall systems. We then
focus on two specific types of 1D spin chains with spins located on the unit
circle, a uniform and an alternating arrangement. For an equidistant
distribution of identical spins we establish an explicit connection to the
SU(N) Haldane-Shastry model, thereby proving that the model is critical and
described by a SU(N) level 1 WZW model. In contrast, while turning out to be
critical as well, the alternating model can only be treated numerically. Our
numerical results rely on a reformulation of the original problem in terms of
loop models.Comment: 37 pages, 6 figure
Topological and symmetry broken phases of Z_N parafermions in one dimension
We classify the gapped phases of Z_N parafermions in one dimension and
construct a representative of each phase. Even in the absence of additional
symmetries besides parafermionic parity, parafermions may be realized in a
variety of phases, one for each divisor n of N. The phases can be characterized
by spontaneous symmetry breaking, topology, or a mixture of the two. Purely
topological phases arise if n is a unitary divisor, i.e. if n and N/n are
co-prime. Our analysis is based on the explicit realization of all symmetry
broken gapped phases in the dual Z_N-invariant quantum spin chains.Comment: 16 pages; v2: improved exposition and additional reference
Classical topological paramagnetism
Topological phases of matter are one of the hallmarks of quantum condensed
matter physics. One of their striking features is a bulk-boundary
correspondence wherein the topological nature of the bulk manifests itself on
boundaries via exotic massless phases. In classical wave phenomena analogous
effects may arise; however, these cannot be viewed as equilibrium phases of
matter. Here we identify a set of rules under which robust equilibrium
classical topological phenomena exist. We write down simple and analytically
tractable classical lattice models of spins and rotors in two and three
dimensions which, at suitable parameter ranges, are paramagnetic in the bulk
but nonetheless exhibit some unusual long-range or critical order on their
boundaries. We point out the role of simplicial cohomology as a means of
classifying, writing-down, and analyzing such models. This opens a new
experimental route for studying strongly interacting topological phases of
spins.Comment: 12 pages + 1 page Appendix; 5 figures; new version with Z_N cas
SEISMIC RESPONSE OF THE NEAR SURFACE QUATERNARY DEPOSITS IN AN AREA BETWEEN THE VENETIAN PRE-ALPS AND THE LAGOON OF VENICE (NORTHEASTERN ITALY)
Rectangular amplitudes, conformal blocks, and applications to loop models
In this paper we continue the investigation of partition functions of
critical systems on a rectangle initiated in [R. Bondesan et al,
Nucl.Phys.B862:553-575,2012]. Here we develop a general formalism of rectangle
boundary states using conformal field theory, adapted to describe geometries
supporting different boundary conditions. We discuss the computation of
rectangular amplitudes and their modular properties, presenting explicit
results for the case of free theories. In a second part of the paper we focus
on applications to loop models, discussing in details lattice discretizations
using both numerical and analytical calculations. These results allow to
interpret geometrically conformal blocks, and as an application we derive new
probability formulas for self-avoiding walks.Comment: 46 page