48 research outputs found
Emergent O(n) Symmetry in a series of three-dimensional Potts Models
We study the q-state Potts model on the simple cubic lattice with
ferromagnetic interactions in one lattice direction, and antiferromagnetic
interactions in the two other directions. As the temperature T decreases, the
system undergoes a second-order phase transition that fits in the universality
class of the 3D O(n) model with n=q-1. This conclusion is based on the
estimated critical exponents, and histograms of the order parameter. At even
smaller T we find, for q=4 and 5, a first-order transition to a phase with a
different type of long-range order. This long-range order dissolves at T=0, and
the system effectively reduces to a disordered two-dimensional Potts
antiferromagnet. These results are obtained by means of Monte Carlo simulations
and finite-size scaling.Comment: 5 pages, 7 figures, accepted by Physical Review
Finite-Size Scaling Theory at a Self-Dual Quantum Critical Point
The nondivergence of the generalized Gr\"uneisen ratio (GR) at a quantum
critical point (QCP) has been proposed to be a universal thermodynamic
signature of self-duality. In this work, we study how the Kramers-Wannier-type
self-duality manifests itself in the finite-size scaling behavior of
thermodynamic quantities in the quantum critical regime. While the self-duality
cannot be realized as a unitary transformation in the total Hilbert space for
the Hamiltonian with the periodic boundary condition, it can be implemented in
certain symmetry sectors with proper boundary conditions. Therefore, the GR and
the transverse magnetization of the one-dimensional transverse-field Ising
model exhibit different finite-size scaling behaviors in different sectors.
This implies that the numerical diagnosis of self-dual QCP requires identifying
the proper symmetry sectors.Comment: 5 pages, 3 figure
Quantum criticality of a symmetric spin chain with long-range interactions
Based on large-scale density matrix renormalization group techniques, we
investigate the critical behaviors of quantum three-state Potts chains with
long-range interactions. Using fidelity susceptibility as an indicator, we
obtain a complete phase diagram of the system. The results show that as the
long-range interaction power increases, the critical points
shift towards lower values. In addition, the critical threshold
) of the long-range interaction power is obtained for
the first time by a non-perturbative numerical method. This indicates that the
critical behavior of the system can be naturally divided into two distinct
universality classes, namely the long-range (\alpha \textless \alpha_c) and
short-range (\alpha \textgreater \alpha_c) universality classes,
qualitatively consistent with the classical effective field theory.
This work provides a useful reference for further research on phase transitions
in quantum spin chains with long-range interaction.Comment: 5+7 pages. Any comments or suggestions are welcome
Special Transition and Extraordinary Phase on the Surface of a Two-Dimensional Quantum Heisenberg Antiferromagnet
Continuous phase transitions exhibit richer critical phenomena on the surface
than in the bulk, because distinct surface universality classes can be realized
at the same bulk critical point by tuning the surface interactions. The
exploration of surface critical behavior provides a window looking into
higher-dimensional boundary conformal field theories. In this work, we study
the surface critical behavior of a two-dimensional (2D) quantum critical
Heisenberg model by tuning the surface coupling strength, and discover a direct
special transition on the surface from the ordinary phase into an extraordinary
phase. The extraordinary phase has a long-range antiferromagnetic order on the
surface, in sharp contrast to the logarithmically decaying spin correlations in
the 3D classical O(3) model. The special transition point has a new set of
critical exponents, and , which are
distinct from the special transition of the classical O(3) model and indicate a
new surface universality class of the 3D O(3) Wilson-Fisher theory.Comment: 5 pages, 3 figures; v2: substantially revised, new fitting form in
extraordinary phas