Disorder line and incommensurate floating phases in the quantum Ising model on an anisotropic triangular lattice

Abstract

We present a Quantum Monte Carlo study of the Ising model in a transverse field on a square lattice with nearest-neighbor antiferromagnetic exchange interaction J and one diagonal secondneighbor interaction J ′ , interpolating between square-lattice (J ′ = 0) and triangular-lattice (J ′ = J) limits. At a transverse-field of Bx = J, the disorder-line first introduced by Stephenson, where the correlations go from Neel to incommensurate, meets the zero temperature axis at J ′ ≈ 0.7J. Strong evidence is provided that the incommensurate phase at larger J ′ , at finite temperatures, is a floating phase with power-law decaying correlations. We sketch a general phase-diagram for such a system and discuss how our work connects with the previous Quantum Monte Carlo work by Isakov and Moessner for the isotropic triangular lattice (J ′ = J). For the isotropic triangular-lattice, we also obtain the entropy function and constant entropy contours using a mix of Quantum Monte Carlo, high-temperature series expansions and high-field expansion methods and show that phase transitions in the model in presence of a transverse field occur at very low entropy.

Thermodynamic description of the Ising antiferromagnet on a triangular lattice with selective dilution by a modified pair-approximation method

“…Equivalency of Eqs. (35) and (36) requires that calculations of the entropy must be consistent with calculations of the correlation function.…”

“…Although frustrated spin systems have been studied in literature for over six decades, they still present a challenging problem for theorists . During recent years the interest in theoretical studies of such systems is still increasing [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. This interest mainly concerns the low-dimensional frustrated magnets which exhibit an intriquing interplay between order and disorder and can reveal existence of new magnetic phases.…”

“…The theoretical studies of low-dimensional frustrated systems have included such structures as: triangular [1,2,6,8,9,11,14,17,24,27,30,31,35,37,40,41], honeycomb [19,25,26,29], square [13,20,36], triangular-square [3], kagomé [10,11,46], pyrochlore [10], penthagonal [33], Shastry-Sutherland lattice [34] and other [47]. Apart from several exact results [1,6,13,33,34,39] most of them have been obtained by the approximate methods, for example: constant coupling method [10], Green function technique [23], spin waves approach [27], cluster theory [8,25,41], Hard-Spin Mean-Field (HSMF) method [7,9], Effective Field Theory (EFT) [24,31]…”

Worm-algorithm-type Simulation of Quantum Transverse-Field Ising Model

“…In higher dimensions, analytical results are scarce, and one has to rely on numerical or approximate methods. Many methods have been developed, including transfer matrix method 9 , series expansion 8,10 , continuous-time Monte Carlo approach 5,[11][12][13][14][15] , tensor renormalization group method 16 , density matrix renormalization group 17 , projected entangledpair states 18 , and machine learning method 19,20 etc. Nevertheless, to obtain a high-precision critical point still remains to be a challenging task.…”