We investigate the evolution of phase transition of the classical fully compact dimer model on the bipartite square lattice with second nearest bonds at finite temperatures. We use the numeric Monte Carlo method with the directed-loop algorithm to simulate the model. Our results show that the order of the phase transition depends on the fugacity of the second nearest bonds. We find that the phase transition reduces from the Kosterlitz-Thouless transition to unconventional high-order phase transitions which feature the coexistence of properties Kosterliz-Thouless transition and the first-order phases transition simultaneously. As the fugacity increases further, phase transition evolves to the first-order phase transition. In addition, our results of dimer-dimer correlation functions and their corresponding structure factor functions computed by us show the evolution of decay correlation for different fugacity.We investigate the evolution of phase transition of the classical fully compact dimer model on the bipartite square lattice with second nearest bonds at finite temperatures. We use the numeric Monte Carlo method with the directed-loop algorithm to simulate the model. Our results show that the order of the phase transition depends on the fugacity of the second nearest bonds. We find that the phase transition reduces from the Kosterlitz-Thouless transition to unconventional high-order phase transitions which feature the coexistence of properties Kosterliz-Thouless transition and the first-order phases transition simultaneously. As the fugacity increases further, phase transition evolves to the first-order phase transition. In addition, our results of dimer-dimer correlation functions and their corresponding structure factor functions computed by us show the evolution of decay correlation for different fugacity.

arXiv:2204.11260Apr 24, 20220 citations

Kosterlitz-Thouless transitions and phase diagrams of the interacting monomer-dimer model on a checkerboard lattice

Sazi Li, Wei Li, Ziyu Chen

Using the tensor network approach, we investigate the monomer-dimer models on a checkerboard lattice, in which there are interactions (with strength $v$ ) between the parallel dimers on half of the plaquettes. For the fully packed interacting dimer model, we observe a Kosterlitz-Thouless (KT) transition between the low-temperature symmetry breaking and the high-temperature critical phases; for the doped monomer-dimer case with finite chemical potential $\ensuremath{\mu}$, we also find an order-disorder phase transition which is of second order instead. We use the boundary matrix product state approach to detect the KT and second-order phase transitions and obtain the phase diagrams $v\text{\ensuremath{-}}T$ and $\ensuremath{\mu}\text{\ensuremath{-}}T$. Moreover, for the noninteracting monomer-dimer model (setting $\ensuremath{\mu}=\ensuremath{\nu}=0$), we get an extraordinarily accurate determination of the free energy per site (negative of the monomer-dimer constant ${h}_{2}$ ) as $f=\ensuremath{-}0.662\phantom{\rule{0.16em}{0ex}}798\phantom{\rule{0.16em}{0ex}}972\phantom{\rule{0.16em}{0ex}}833\phantom{\rule{0.16em}{0ex}}746$ with the dimer density $n=0.638\phantom{\rule{0.16em}{0ex}}123\phantom{\rule{0.16em}{0ex}}109\phantom{\rule{0.16em}{0ex}}228\phantom{\rule{0.16em}{0ex}}547$ , both of 15 correct digits.Using the tensor network approach, we investigate the monomer-dimer models on a checkerboard lattice, in which there are interactions (with strength $v$) between the parallel dimers on half of the plaquettes. For the fully packed interacting dimer model, we observe a Kosterlitz-Thouless (KT) transition between the low-temperature symmetry breaking and the high-temperature critical phases; for the doped monomer-dimer case with finite chemical potential $\ensuremath{\mu}$, we also find an order-disorder phase transition which is of second order instead. We use the boundary matrix product state approach to detect the KT and second-order phase transitions and obtain the phase diagrams $v\text{\ensuremath{-}}T$ and $\ensuremath{\mu}\text{\ensuremath{-}}T$. Moreover, for the noninteracting monomer-dimer model (setting $\ensuremath{\mu}=\ensuremath{\nu}=0$), we get an extraordinarily accurate determination of the free energy per site (negative of the monomer-dimer constant ${h}_{2}$) as $f=\ensuremath{-}0.662\phantom{\rule{0.16em}{0ex}}798\phantom{\rule{0.16em}{0ex}}972\phantom{\rule{0.16em}{0ex}}833\phantom{\rule{0.16em}{0ex}}746$ with the dimer density $n=0.638\phantom{\rule{0.16em}{0ex}}123\phantom{\rule{0.16em}{0ex}}109\phantom{\rule{0.16em}{0ex}}228\phantom{\rule{0.16em}{0ex}}547$, both of 15 correct digits.

arXiv:1504.01565Physical Review ENov 5, 20144 citations

Quantum Dimer Model: Phase Diagrams

Garry Goldstein, Claudio Chamon, Claudio Castelnovo

Bulletin of the American Physical SocietyMar 14, 20160 citations

First-order quantum phase transition in the orthogonal-dimer spin chain

昌久古賀, Akihisa Koga

Jan 1, 20000 citations

Renormalization, duality, and phase transitions in two- and three-dimensional quantum dimer models

Flavio S. Nogueira, Zohar Nussinov

We derive an extended lattice gauge theory type action for quantum dimer models and relate it to the height representations of these systems. We examine the system in two and three dimensions and analyze the phase structure in terms of effective theories and duality arguments. For the two-dimensional case we derive the effective potential both at zero and finite temperature. The zero-temperature theory at the Rokhsar-Kivelson (RK) point has a critical point related to the self-dual point of a class of ${Z}_{N}$ models in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. Two phase transitions featuring a fixed line are shown to appear in the phase diagram, one at zero temperature and at the RK point and another one at finite temperature above the RK point. The latter will be shown to correspond to a Kosterlitz-Thouless (KT) phase transition, while the former will be governed by a KT-like universality class, i.e., sharing many features with a KT transition but actually corresponding to a different universality class. On the other hand, we show that at the RK point no phase transition happens at finite temperature. For the three-dimensional case we derive the corresponding dual gauge theory model at the RK point. We show in this case that at zero temperature a first-order phase transition occurs, while at finite temperatures both first- and second-order phase transitions are possible, depending on the relative values of the couplings involved.We derive an extended lattice gauge theory type action for quantum dimer models and relate it to the height representations of these systems. We examine the system in two and three dimensions and analyze the phase structure in terms of effective theories and duality arguments. For the two-dimensional case we derive the effective potential both at zero and finite temperature. The zero-temperature theory at the Rokhsar-Kivelson (RK) point has a critical point related to the self-dual point of a class of ${Z}_{N}$ models in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. Two phase transitions featuring a fixed line are shown to appear in the phase diagram, one at zero temperature and at the RK point and another one at finite temperature above the RK point. The latter will be shown to correspond to a Kosterlitz-Thouless (KT) phase transition, while the former will be governed by a KT-like universality class, i.e., sharing many features with a KT transition but actually corresponding to a different universality class. On the other hand, we show that at the RK point no phase transition happens at finite temperature. For the three-dimensional case we derive the corresponding dual gauge theory model at the RK point. We show in this case that at zero temperature a first-order phase transition occurs, while at finite temperatures both first- and second-order phase transitions are possible, depending on the relative values of the couplings involved.

arXiv:0812.3903Physical Review BSep 11, 200915 citations

Using the tensor network approach, we investigate the monomer-dimer models on a checkerboard lattice, in which there are interactions (with strength

v

) between the parallel dimers on half of the plaquettes. For the fully packed interacting dimer model, we observe a Kosterlitz-Thouless (KT) transition between the low-temperature symmetry breaking and the high-temperature critical phases; for the doped monomer-dimer case with finite chemical potential $\ensuremath{\mu}$, we also find an order-disorder phase transition which is of second order instead. We use the boundary matrix product state approach to detect the KT and second-order phase transitions and obtain the phase diagrams $v\text{\ensuremath{-}}T$ and $\ensuremath{\mu}\text{\ensuremath{-}}T$. Moreover, for the noninteracting monomer-dimer model (setting $\ensuremath{\mu}=\ensuremath{\nu}=0$), we get an extraordinarily accurate determination of the free energy per site (negative of the monomer-dimer constant

{h}_{2}

) as $f=\ensuremath{-}0.662\phantom{\rule{0.16em}{0ex}}798\phantom{\rule{0.16em}{0ex}}972\phantom{\rule{0.16em}{0ex}}833\phantom{\rule{0.16em}{0ex}}746$ with the dimer density

n=0.638\phantom{\rule{0.16em}{0ex}}123\phantom{\rule{0.16em}{0ex}}109\phantom{\rule{0.16em}{0ex}}228\phantom{\rule{0.16em}{0ex}}547

, both of 15 correct digits.

{Z}_{N}

models in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. Two phase transitions featuring a fixed line are shown to appear in the phase diagram, one at zero temperature and at the RK point and another one at finite temperature above the RK point. The latter will be shown to correspond to a Kosterlitz-Thouless (KT) phase transition, while the former will be governed by a KT-like universality class, i.e., sharing many features with a KT transition but actually corresponding to a different universality class. On the other hand, we show that at the RK point no phase transition happens at finite temperature. For the three-dimensional case we derive the corresponding dual gauge theory model at the RK point. We show in this case that at zero temperature a first-order phase transition occurs, while at finite temperatures both first- and second-order phase transitions are possible, depending on the relative values of the couplings involved.