Interfaces, strings, and a soft mode in the square lattice quantum dimer model

Abstract

The quantum dimer model on the square lattice is equivalent to a U (1) gauge theory. Quantum Monte Carlo calculations reveal that, for values of the Rokhsar-Kivelson (RK) coupling λ < 1, the theory exists in a confining columnar phase. The interfaces separating distinct columnar phases display plaquette order, which, however, is not realized as a bulk phase. Static "electric" charges are confined by flux tubes that consist of multiple strands, each carrying a fractionalized flux 1 4 . A soft pseudo-Goldstone mode emerges around λ ≈ 0, long before one reaches the RK point at λ = 1.

Finite-volume energy spectrum, fractionalized strings, and low-energy effective field theory for the quantum dimer model on the square lattice

“…We would like to point out that many of the analytical results of the present manuscript never appeared in Ref. [19], hence are new. In particular, one new Monte Carlo result with intriguing physics is shown in present manuscript as well.…”

Engineering SU(2) invariant spin models to mimic quantum dimer physics on the square lattice

“…Presumably, the system sizes that can be reached are too small to give any reliable information on the thermodynamic limit because of the existing diverging length close to RK point. 30,31 While in principle, the supplementary terms (t 6 , v 6 etc) induced by the non-trivial singlet dynamics in H K,θ could favor one particular type of ordering, we cannot make either any definitive statement on the behavior in the thermodynamic limit for the point θ B , based on our finite cluster simulations. This is confirmed by computations of correlations in Fig.…”

“…29 However, in the case of the QDM, there is no clear gap above these eight states and refined ED and QMC studies have found no evidence for such mixed phase: 30,31 it is instead indicative of a U(1) regime where no crystalline order is frozen yet (on the available system sizes). Presumably, the system sizes that can be reached are too small to give any reliable information on the thermodynamic limit because of the existing diverging length close to RK point.…”

“…in a region where the columnar order is not fully established yet even using large-scale quantum Monte-Carlo simulations. 30,31 Fig. 6(b) presents the low-energy spectra where we observe in ED and NNVB computations and GQDM spectra, that both set of states expected to construct columnar or plaquette states in the thermodynamic limit are present at low-energy.…”

“…In the intermediate region, a plaquette phase has been suggested to exist, [26][27][28] or a mixed columnar-plaquette, 29 but its presence has recently been questioned and the columnar phase seems to extend up to the RK point. 30,31 Of course larger loops processes, in particular t 6 (θ), must also be taken into account and can somehow modify this simple picture. A careful numerical study ofĤ K,θ should therefore be pursued, which will be done using both exact and NNVB diagonalization, together with an exact diagonalization study of the GQDM counterpart.…”