arXiv:1310.3468

Reentrant Berezinskii-Kosterlitz-Thouless Transition in a Triangular Ising Thin Film

Shi‐Zeng Lin, Yoshitomo Kamiya, Gia-Wei Chern, Cristian D. Batista

Published Oct 13, 2013• 0 citations

Abstract

We study the triangular lattice Ising model with a finite number of vertically stacked layers. By combining analytical and numerical results, we demonstrate a low temperature reentrance of two Berezinskii-Kosterlitz-Thouless transitions that results in an extended disordered regime down to T=0. We introduce an effective theory that quantitatively describes the low temperature physics emerging from the extensively degenerate ground state manifold and explain the global qualitative features of the phase diagram by mapping the classical spin model into the single-layer quantum Ising model.

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arXiv:1310.3468

Reentrant Berezinskii-Kosterlitz-Thouless Transition in a Triangular Ising Thin Film

Shi‐Zeng Lin, Yoshitomo Kamiya, Gia-Wei Chern, Cristian D. Batista

Published Oct 13, 2013• 0 citations

arXiv HTML PDF

Abstract

Related papers

Phase diagram of the quantum Ising model on a triangular lattice under external field

Yuan Da Liao, Han Li, Zheng Yan +4 more

Quantum Ising model on a triangular lattice hosts a finite temperature Berezinskii-Kosterlitz-Thouless (BKT) phase with emergent U(1) symmetry, and it will transit into an up-up-down (UUD) phase with ${C}_{3}$ symmetry breaking upon an infinitesimal external field along the longitudinal direction, but the overall phase diagram spanned by the axes of external field and temperature remains opaque due to the lack of systematic investigations with controlled methodologies. By means of quantum Monte Carlo at finite temperature and ground state density matrix renormalization group simulations, we map out the phase diagram of triangular quantum Ising model. Starting from the upper BKT temperature at zero field, we obtain the phase boundary between the UUD and paramagnetic phases with its 2D $q=3$ Potts universality at weak field and weakly first order transition at strong field. Originated from the lower BKT temperature at zero field, we analyze the low temperature phase boundary between the clock phase and the UUD phase with Ising symmetry breaking at weak fields and the quantum phase transition between the UUD and fully polarized phases at strong fields. The accurate many-body numerical results are consistent with our field theoretical analysis. The experimental relevance towards the BKT magnet ${\mathrm{TmMgGaO}}_{4}$ and programmable quantum simulators are also discussed.Quantum Ising model on a triangular lattice hosts a finite temperature Berezinskii-Kosterlitz-Thouless (BKT) phase with emergent U(1) symmetry, and it will transit into an up-up-down (UUD) phase with ${C}_{3}$ symmetry breaking upon an infinitesimal external field along the longitudinal direction, but the overall phase diagram spanned by the axes of external field and temperature remains opaque due to the lack of systematic investigations with controlled methodologies. By means of quantum Monte Carlo at finite temperature and ground state density matrix renormalization group simulations, we map out the phase diagram of triangular quantum Ising model. Starting from the upper BKT temperature at zero field, we obtain the phase boundary between the UUD and paramagnetic phases with its 2D $q=3$ Potts universality at weak field and weakly first order transition at strong field. Originated from the lower BKT temperature at zero field, we analyze the low temperature phase boundary between the clock phase and the UUD phase with Ising symmetry breaking at weak fields and the quantum phase transition between the UUD and fully polarized phases at strong fields. The accurate many-body numerical results are consistent with our field theoretical analysis. The experimental relevance towards the BKT magnet ${\mathrm{TmMgGaO}}_{4}$ and programmable quantum simulators are also discussed.

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Quantum Ising model on a triangular lattice hosts a finite temperature Berezinskii-Kosterlitz-Thouless (BKT) phase with emergent U(1) symmetry, and it will transit into an up-up-down (UUD) phase with

{C}_{3}

symmetry breaking upon an infinitesimal external field along the longitudinal direction, but the overall phase diagram spanned by the axes of external field and temperature remains opaque due to the lack of systematic investigations with controlled methodologies. By means of quantum Monte Carlo at finite temperature and ground state density matrix renormalization group simulations, we map out the phase diagram of triangular quantum Ising model. Starting from the upper BKT temperature at zero field, we obtain the phase boundary between the UUD and paramagnetic phases with its 2D

q=3

Potts universality at weak field and weakly first order transition at strong field. Originated from the lower BKT temperature at zero field, we analyze the low temperature phase boundary between the clock phase and the UUD phase with Ising symmetry breaking at weak fields and the quantum phase transition between the UUD and fully polarized phases at strong fields. The accurate many-body numerical results are consistent with our field theoretical analysis. The experimental relevance towards the BKT magnet

{\mathrm{TmMgGaO}}_{4}

and programmable quantum simulators are also discussed.

Using Monte Carlo simulations and finite-size scaling, we study a three-state Potts antiferromagnet on a layered square lattice with two and four layers:

{L}_{z}=2

and 4, respectively. As temperature decreases, the system develops quasi-long-range order via a Berezinskii-Kosterlitz-Thouless transition at finite temperature

{T}_{c1}

. For

{L}_{z}=4

, as temperature is further lowered, a long-range order breaking the

{Z}_{6}

symmetry develops at a second transition at

{T}_{c2}<{T}_{c1}

. The transition at

{T}_{c2}

is also Berezinskii-Kosterlitz-Thouless-like, but has a magnetic critical exponent $\ensuremath{\eta}=1/9$ instead of the conventional value $\ensuremath{\eta}=1/4$. The emergent

U(1)

symmetry is clearly demonstrated in the quasi-long-range ordered region ${T}_{c2}\ensuremath{\le}T\ensuremath{\le}{T}_{c1}$.

{\mathrm{S}}_{\mathrm{L}}

\ensuremath{\leqslant}3. The phase diagram at finite temperatures is also discussed.

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition in two-dimensional planar rotator and

XY

models on a square lattice, diluted by randomly placed vacancies, is studied here using hybrid Monte Carlo simulations that combine single spin flip, cluster, and over-relaxation techniques. The transition temperature

{T}_{c}

is determined as a function of vacancy density ${\ensuremath{\rho}}_{\mathrm{vac}}$ by finite-size scaling of the helicity modulus and the in-plane magnetic susceptibility. The results for

{T}_{c}

are consistent with those from the much less precise fourth-order cumulant of Binder.

{T}_{c}

is found to decrease monotonically with increasing ${\ensuremath{\rho}}_{\mathrm{vac}}$, and falls to zero close to the square lattice percolation limit, ${\ensuremath{\rho}}_{\mathrm{vac}}\ensuremath{\approx}0.41$. The result is physically reasonable: the quasi-long-range orientational order of the low-temperature phase cannot be maintained in the absence of sufficient spin interactions across the lattice.

x

-polarized phase, stripe-ordered phases, and clock-ordered phases which emerge from an order-by-disorder scenario already present in the nearest-neighbor model. In addition, the generic presence of a potential intermediate gapless phase with algebraic correlations and associated Kosterlitz-Thouless transitions is discussed for both cylinders.