arXiv subjects

Scott D. Geraedts

Publications and source records attributed to Scott D. Geraedts.

23 records · Page 2Linked to original sources

arXiv2012

Monte Carlo Study of a $U(1)\times U(1)$ Loop Model with Modular Invariance

We study a $U(1)\times U(1)$ system in (2+1)-dimensions with long-range interactions and mutual statistics. The model has the same form after the application of operations from the modular group, a property which we call modular invariance. Using the modular invariance of the model, we propose a possible phase diagram. We obtain a sign-free reformulation of the model and study it in Monte Carlo. This study confirms our proposed phase diagram. We use the modular invariance to analytically determine the current-current correlation functions and conductivities in all the phases in the diagram, as well as at special "fixed" points which are unchanged by an operation from the modular group. We numerically determine the order of the phase transitions, and find segments of second-order transitions. For the statistical interaction parameter $θ=π$, these second-order transitions are evidence of a critical loop phase obtained when both loops are trying to condense simulataneously. We also measure the critical exponents of the second-order transitions.

cond-mat.stat-mech↗

arXiv2012

Phases and phase transitions in a $U(1)\times U(1)$ system with $θ=2π/3$ mutual statistics

We study a $U(1)\times U(1)$ system with short-range interactions and mutual $θ=2π/3$ statistics in (2+1) dimensions. We are able to reformulate the model to eliminate the sign problem, and perform a Monte Carlo study. We find a phase diagram containing a phase with only small loops and two phases with one species of proliferated loop. We also find a phase where both species of loop condense, but without any gapless modes. Lastly, when the energy cost of loops becomes small we find a phase which is a condensate of bound states, each made up of three particles of one species and a vortex of the other. We define several exact reformulations of the model, which allow us to precisely describe each phase in terms of gapped excitations. We propose field-theoretic descriptions of the phases and phase transitions, which are particularly interesting on the "self-dual" line where both species have identical interactions. We also define irreducible responses useful for describing the phases.

cond-mat.stat-mech↗

arXiv2012

Line of continuous phase transitions in a three dimensional U(1) model with 1/r^2 current-current interactions

We study a lattice model of interacting loops in three dimensions with a $1/r^2$ interaction. Using Monte Carlo, we find that the phase diagram contains a line of second-order phase transitions between a phase where the loops are gapped and a phase where they proliferate. The correlation length exponent and critical conductivity vary continuously along this line. Our model is exactly self-dual at a special point on the critical line, which allows us to calculate the critical conductivity exactly at this point.

cond-mat.stat-mech↗

arXiv2011

Monte Carlo Study of a U(1)xU(1) system with π-statistical Interaction

We study a $U(1)\times U(1)$ system with two species of loops with mutual $π$-statistics in (2+1) dimensions. We are able to reformulate the model in a way that can be studied by Monte Carlo and we determine the phase diagram. In addition to a phase with no loops, we find two phases with only one species of loop proliferated. The model has a self-dual line, a segment of which separates these two phases. Everywhere on the segment, we find the transition to be first-order, signifying that the two loop systems behave as immiscible fluids when they are both trying to condense. Moving further along the self-dual line, we find a phase where both loops proliferate, but they are only of even strength, and therefore avoid the statistical interactions. We study another model which does not have this phase, and also find first-order behavior on the self-dual segment.

cond-mat.stat-mech↗

arXiv2010

Exact Results for the Bipartite Entanglement Entropy of the AKLT spin-1 chain

We study the entanglement between two domains of a spin-1 AKLT chain subject to open boundary conditions. In this case the ground-state manifold is four-fold degenerate. We summarize known results and present additional exact analytical results for the von Neumann entanglement entropy, as a function of both the size of the domains and the total system size for {\it all} four degenerate ground-states. In the large $l,L$ limit the entanglement entropy approaches $\ln(2)$ and $2\ln(2)$ for the $S^z_T=\pm 1$ and $S^z_T=0$ states, respectively. In all cases, it is found that this constant is approached exponentially fast defining a length scale $ξ=1/\ln(3)$ equal to the known bulk correlation length.

cond-mat.stat-mech↗