Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userO(3) model with Nienhuis action
94
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the O(3) sigma model in $D=2$ on the lattice with a Boltzmann weight linearized in $beta$ on each link. While the spin formulation now suffers from a sign-problem the equivalent loop model remains positive and becomes particularly simple. By studying the transfer matrix and by performing Monte Carlo simulations in the loop form we study the mass gap coupling in a step scaling analysis. The question addressed is, whether or not such a simplified action still has the right universal continuum limit. If the answer is affirmative this would be helpful in widening the applicability of worm algorithm methods.
rate research
Read More
The 2d O(3) model is widely used as a toy model for ferromagnetism and for Quantum Chromodynamics. With the latter it shares --- among other basic aspects --- the property that the continuum functional integral splits into topological sectors. Topology can also be defined in its lattice regularised version, but semi-classical arguments suggest that the topological susceptibility $chi_{rm t}$ does not scale towards a finite continuum limit. Previous numerical studies confirmed that the quantity $chi_{rm t}, xi^{2}$ diverges at large correlation length $xi$. Here we investigate the question whether or not this divergence persists when the configurations are smoothened by the Gradient Flow (GF). The GF destroys part of the topological windings; on fine lattices this strongly reduces $chi_{rm t}$. However, even when the flow time is so long that the GF impact range --- or smoothing radius --- attains $xi/2$, we do still not observe evidence of continuum scaling.
The $SU(3)$ spin model with chemical potential corresponds to a simplified version of QCD with static quarks in the strong coupling regime. It has been studied previously as a testing ground for new methods aiming to overcome the sign problem of lattice QCD. In this work we show that the equation of state and the phase structure of the model can be determined to reasonable accuracy by a linked cluster expansion. In particular, we compute the free energy to 14-th order in the nearest neighbour coupling. The resulting predictions for the equation of state and the location of the critical end point agree with numerical determinations to ${cal O}(1%)$ and ${cal O}(10%)$, respectively. While the accuracy for the critical couplings is still limited at the current series depth, the approach is equally applicable at zero and non-zero imaginary or real chemical potential, as well as to effective QCD Hamiltonians obtained by strong coupling and hopping expansions.
We connect explicitly the classical $O(2)$ model in 1+1 dimensions, a model sharing important features with $U(1)$ lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization group formulation, we take the time continuum limit and check that finite dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a $^{87}$Rb and $^{41}$K Bose-Bose mixture.
We calculate thermodynamic potentials and their derivatives for the three-dimensional $O(2)$ model using tensor-network methods to investigate the well-known second-order phase transition. We also consider the model at non-zero chemical potential to study the Silver Blaze phenomenon, which is related to the particle number density at zero temperature. Furthermore, the temperature dependence of the number density is explored using asymmetric lattices. Our results for both zero and non-zero magnetic field, temperature, and chemical potential are consistent with those obtained using other methods.
Motivated by recent attempts to quantum simulate lattice models with continuous Abelian symmetries using discrete approximations, we define an extended-O(2) model by adding a $gamma cos(qvarphi)$ term to the ordinary O(2) model with angular values restricted to a $2pi$ interval. In the $gamma rightarrow infty$ limit, the model becomes an extended $q$-state clock model that reduces to the ordinary $q$-state clock model when $q$ is an integer and otherwise is a continuation of the clock model for noninteger $q$. By shifting the $2pi$ integration interval, the number of angles selected can change discontinuously and two cases need to be considered. What we call case $1$ has one more angle than what we call case $2$. We investigate this class of clock models in two space-time dimensions using Monte Carlo and tensor renormalization group methods. Both the specific heat and the magnetic susceptibility show a double-peak structure for fractional $q$. In case $1$, the small-$beta$ peak is associated with a crossover, and the large-$beta$ peak is associated with an Ising critical point, while both peaks are crossovers in case $2$. When $q$ is close to an integer by an amount $Delta q$ and the system is close to the small-$beta$ Berezinskii-Kosterlitz-Thouless transition, the system has a magnetic susceptibility that scales as $sim 1 / (Delta q)^{1 - 1/delta}$ with $delta$ estimates consistent with the magnetic critical exponent $delta = 15$. The crossover peak and the Ising critical point move to Berezinskii-Kosterlitz-Thouless transition points with the same power-law scaling. A phase diagram for this model in the $(beta, q)$ plane is sketched. These results are possibly relevant for configurable Rydberg-atom arrays where the interpolations among phases with discrete symmetries can be achieved by varying continuously the distances among atoms and the detuning frequency.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
