Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0501241 · Physical Review Letters

Interacting Classical Dimers on the Square Lattice

Fabien Alet, Jesper Lykke Jacobsen, Grégoire Misguich, Vincent Pasquier, Frédéric Mila, Matthias Troyer

Published Jun 15, 2005• 116 citations
arXivHTMLPDF

Abstract

We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988)]. By means of Monte Carlo and transfer matrix calculations, we show that this system undergoes a Kosterlitz-Thouless transition separating a low temperature ordered phase where dimers are aligned in columns from a high temperature critical phase with continuously varying exponents. This is understood by constructing the corresponding Coulomb gas, whose coupling constant is computed numerically. We also discuss doped models and implications on the finite-temperature phase diagram of quantum dimer models.

DOI
10.1103/physrevlett.94.235702

Related papers

Classical dimers with aligning interactions on the square lattice

Fabien Alet, Yacine Ikhlef, Jesper Lykke Jacobsen +2 more

We present a detailed study of a model of close-packed dimers on the square lattice with an interaction between nearest-neighbor dimers. The interaction favors parallel alignment of dimers, resulting in a low-temperature crystalline phase. With large-scale Monte Carlo and transfer matrix calculations, we show that the crystal melts through a Kosterlitz-Thouless phase transition to give rise to a high-temperature critical phase, with algebraic decays of correlations functions with exponents that vary continuously with the temperature. We give a theoretical interpretation of these results by mapping the model to a Coulomb gas, whose coupling constant and associated exponents are calculated numerically with high precision. Introducing monomers is a marginal perturbation at the Kosterlitz-Thouless transition and gives rise to another critical line. We study this line numerically, showing that it is in the Ashkin-Teller universality class, and terminates in a tricritical point at finite temperature and monomer fugacity. In the course of this work, we also derive analytic results relevant to the noninteracting case of dimer coverings, including a Bethe ansatz (at the free fermion point) analysis, a detailed discussion of the effective height model, and a free field analysis of height fluctuations.

arXiv:cond-mat/0607747•Physical Review E•Oct 26, 2006•106 citations

Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models

Stefanos Papanikolaou, Erik Luijten, Eduardo Fradkin

We study phase diagrams of a class of doped quantum dimer models on the square lattice with ground-state wave functions whose amplitudes have the form of the Gibbs weights of a classical doped dimer model. In this dimer model, parallel neighboring dimers have attractive interactions, whereas neighboring holes either do not interact or have a repulsive interaction. We investigate the behavior of this system via analytic methods and by Monte Carlo simulations. At zero doping, we confirm the existence of a Kosterlitz-Thouless transition from a quantum critical phase to a columnar phase. At low hole densities, we find a dimer-hole liquid phase and a columnar phase, separated by a phase boundary which is a line of critical points with varying exponents. We demonstrate that this line ends at a multicritical point where the transition becomes first order and the system phase separates. The first-order transition coexistence curve is shown to become unstable with respect to more complex inhomogeneous phases in the presence of direct hole-hole interactions. We also use a variational approach to determine the spectrum of low-lying density fluctuations in the dimer-hole fluid phase.

arXiv:cond-mat/0607316•Physical Review B•Oct 24, 2007•74 citations

Reentrance effect in the high-temperature critical phase of the quantum dimer model on the square lattice

Bhupen Dabholkar, G. J. Sreejith, Fabien Alet

We present a quantum Monte Carlo investigation of the finite-temperature phase diagram of the quantum dimer model on the square lattice. We use the sweeping cluster algorithm, which allows the exact implementation of the dimer constraint, supplemented with an equal-time directed loop move that allows sampling the winding sectors. We find a high-temperature critical phase with power-law correlations that extends down to the Rokhsar-Kivelson point, in the vicinity of which a reentrance effect in the lines of constant exponent is found. For small values of the kinetic energy strength, we find finite-temperature transitions to ordered states (columnar and staggered) which match those of interacting classical dimer models.

arXiv:2207.03301•Physical review. B./Physical review. B•Nov 14, 2022•7 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.

arXiv:1504.01565•Physical Review E•Nov 5, 2014•4 citations

Ising nematic fluid phase of hard-core dimers on the square lattice

Stefanos Papanikolaou, D. Charrier, Eduardo Fradkin

We present a model of classical hard-core dimers on the square lattice that contains an Ising nematic phase in its phase diagram. We consider a model with an attractive interaction for parallel dimers on a given plaquette of the square lattice and an attractive interaction for neighboring parallel dimers on the same row (viz column) of the lattice. By extensive Monte Carlo simulations we find that with a finite density of holes the phase diagram has, with rising temperatures, a columnar crystalline phase, an Ising nematic liquid phase and a disordered fluid phase, separated by Ising continuous phase transitions. We present strong evidence for the Ising universality class of both transitions. The Ising nematic phase can be interpreted as either an intermediate classical thermodynamic phase (possibly of a strongly correlated antiferromagnet) or as a phase of a two-dimensional quantum dimer model using the Rokhsar-Kivelson construction of exactly solvable quantum Hamiltonians.

arXiv:1310.4173•Physical Review B•Jan 21, 2014•7 citations

Doping quantum dimer models on the square lattice

Didier Poilblanc, Fabien Alet, Federico Becca +3 more

A family of models is proposed to describe the motion of holes in a fluctuating quantum dimer background on the square lattice. Following Castelnovo et al. [Ann. Phys. (N.Y.) 318, 316 (2005)], a generalized Rokhsar-Kivelson Hamiltonian at finite doping which can be mapped on a doped interacting classical dimer model is constructed. A simple physical extension of this model is also considered. Using numerical computations and simple considerations based on the above exact mapping, we determine the phase diagram of the model showing a number of quantum phases typical of a doped Mott insulator. The two-hole correlation function generically exhibits short-range or long-range algebraic correlations in the solid (columnar) and liquid (critical) phases of the model, respectively. Evidence for an extended region of a doped valence bond solid phase exhibiting holon pairing but no phase separation is given. In contrast, we show that hole deconfinement occurs in the staggered dimer phase.

arXiv:cond-mat/0602256•Physical Review B•Jul 26, 2006•20 citations
We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988)]. By means of Monte Carlo and transfer matrix calculations, we show that this system undergoes a Kosterlitz-Thouless transition separating a low temperature ordered phase where dimers are aligned in columns from a high temperature critical phase with continuously varying exponents. This is understood by constructing the corresponding Coulomb gas, whose coupling constant is computed numerically. We also discuss doped models and implications on the finite-temperature phase diagram of quantum dimer models.
We present a detailed study of a model of close-packed dimers on the square lattice with an interaction between nearest-neighbor dimers. The interaction favors parallel alignment of dimers, resulting in a low-temperature crystalline phase. With large-scale Monte Carlo and transfer matrix calculations, we show that the crystal melts through a Kosterlitz-Thouless phase transition to give rise to a high-temperature critical phase, with algebraic decays of correlations functions with exponents that vary continuously with the temperature. We give a theoretical interpretation of these results by mapping the model to a Coulomb gas, whose coupling constant and associated exponents are calculated numerically with high precision. Introducing monomers is a marginal perturbation at the Kosterlitz-Thouless transition and gives rise to another critical line. We study this line numerically, showing that it is in the Ashkin-Teller universality class, and terminates in a tricritical point at finite temperature and monomer fugacity. In the course of this work, we also derive analytic results relevant to the noninteracting case of dimer coverings, including a Bethe ansatz (at the free fermion point) analysis, a detailed discussion of the effective height model, and a free field analysis of height fluctuations.
We study phase diagrams of a class of doped quantum dimer models on the square lattice with ground-state wave functions whose amplitudes have the form of the Gibbs weights of a classical doped dimer model. In this dimer model, parallel neighboring dimers have attractive interactions, whereas neighboring holes either do not interact or have a repulsive interaction. We investigate the behavior of this system via analytic methods and by Monte Carlo simulations. At zero doping, we confirm the existence of a Kosterlitz-Thouless transition from a quantum critical phase to a columnar phase. At low hole densities, we find a dimer-hole liquid phase and a columnar phase, separated by a phase boundary which is a line of critical points with varying exponents. We demonstrate that this line ends at a multicritical point where the transition becomes first order and the system phase separates. The first-order transition coexistence curve is shown to become unstable with respect to more complex inhomogeneous phases in the presence of direct hole-hole interactions. We also use a variational approach to determine the spectrum of low-lying density fluctuations in the dimer-hole fluid phase.
We present a quantum Monte Carlo investigation of the finite-temperature phase diagram of the quantum dimer model on the square lattice. We use the sweeping cluster algorithm, which allows the exact implementation of the dimer constraint, supplemented with an equal-time directed loop move that allows sampling the winding sectors. We find a high-temperature critical phase with power-law correlations that extends down to the Rokhsar-Kivelson point, in the vicinity of which a reentrance effect in the lines of constant exponent is found. For small values of the kinetic energy strength, we find finite-temperature transitions to ordered states (columnar and staggered) which match those of interacting classical dimer models.
Using the tensor network approach, we investigate the monomer-dimer models on a checkerboard lattice, in which there are interactions (with strength vvv) 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 h2{h}_{2}h2​) 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=0.638123109228547n=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}}547n=0.638123109228547, both of 15 correct digits.
We present a model of classical hard-core dimers on the square lattice that contains an Ising nematic phase in its phase diagram. We consider a model with an attractive interaction for parallel dimers on a given plaquette of the square lattice and an attractive interaction for neighboring parallel dimers on the same row (viz column) of the lattice. By extensive Monte Carlo simulations we find that with a finite density of holes the phase diagram has, with rising temperatures, a columnar crystalline phase, an Ising nematic liquid phase and a disordered fluid phase, separated by Ising continuous phase transitions. We present strong evidence for the Ising universality class of both transitions. The Ising nematic phase can be interpreted as either an intermediate classical thermodynamic phase (possibly of a strongly correlated antiferromagnet) or as a phase of a two-dimensional quantum dimer model using the Rokhsar-Kivelson construction of exactly solvable quantum Hamiltonians.
A family of models is proposed to describe the motion of holes in a fluctuating quantum dimer background on the square lattice. Following Castelnovo et al. [Ann. Phys. (N.Y.) 318, 316 (2005)], a generalized Rokhsar-Kivelson Hamiltonian at finite doping which can be mapped on a doped interacting classical dimer model is constructed. A simple physical extension of this model is also considered. Using numerical computations and simple considerations based on the above exact mapping, we determine the phase diagram of the model showing a number of quantum phases typical of a doped Mott insulator. The two-hole correlation function generically exhibits short-range or long-range algebraic correlations in the solid (columnar) and liquid (critical) phases of the model, respectively. Evidence for an extended region of a doped valence bond solid phase exhibiting holon pairing but no phase separation is given. In contrast, we show that hole deconfinement occurs in the staggered dimer phase.