The $\mathbb{Z}_2$ topological phase in the quantum dimer model on the Kagomé-lattice is a candidate for the description of the low-energy physics of the anti-ferromagnetic Heisenberg model on the same lattice. We study the extend of the topological phase by interpolating between the exactly solvable parent Hamiltonian of the topological phase and an effective low-energy description of the Heisenberg model in terms of a quantum-dimer Hamiltonian. Therefore, we perform a perturbative treatment of the low-energy excitations in the topological phase including free and interacting quasi-particles. We find a phase transition out of the topological phase far from the Heisenberg point. The resulting phase is characterized by a spontaneously broken rotational symmetry and a unit cell involving six sites.The $\mathbb{Z}_2$ topological phase in the quantum dimer model on the Kagomé-lattice is a candidate for the description of the low-energy physics of the anti-ferromagnetic Heisenberg model on the same lattice. We study the extend of the topological phase by interpolating between the exactly solvable parent Hamiltonian of the topological phase and an effective low-energy description of the Heisenberg model in terms of a quantum-dimer Hamiltonian. Therefore, we perform a perturbative treatment of the low-energy excitations in the topological phase including free and interacting quasi-particles. We find a phase transition out of the topological phase far from the Heisenberg point. The resulting phase is characterized by a spontaneously broken rotational symmetry and a unit cell involving six sites.

arXiv:1712.06699Dec 18, 20170 citations

Topological entanglement entropy in the quantum dimer model on the triangular lattice

Shunsuke Furukawa, Grégoire Misguich

A characterization of topological order in terms of bi-partite entanglement was proposed recently [A. Kitaev and J. Preskill, Phys. Rev. Lett. 96, 110404 (2006); M. Levin and X.-G. Wen, ibid. 96, 110405 (2006)]. It was argued that in a topological phase there is a universal additive constant in the entanglement entropy, called the topological entanglement entropy, which reflects the underlying gauge theory for the topological order. In the present paper, we evaluate numerically the topological entanglement entropy in the ground states of a quantum dimer model on the triangular lattice, which is known to have a dimer liquid phase with ${\mathbb{Z}}_{2}$ topological order. We examine the two original constructions to measure the topological entropy by combining entropies on plural areas, and we observe that in the large-area limit they both approach the value expected for ${\mathbb{Z}}_{2}$ topological order. We also consider the entanglement entropy on a topologically nontrivial ``zigzag'' area and propose to use it as another way to measure the topological entropy.A characterization of topological order in terms of bi-partite entanglement was proposed recently [A. Kitaev and J. Preskill, Phys. Rev. Lett. 96, 110404 (2006); M. Levin and X.-G. Wen, ibid. 96, 110405 (2006)]. It was argued that in a topological phase there is a universal additive constant in the entanglement entropy, called the topological entanglement entropy, which reflects the underlying gauge theory for the topological order. In the present paper, we evaluate numerically the topological entanglement entropy in the ground states of a quantum dimer model on the triangular lattice, which is known to have a dimer liquid phase with ${\mathbb{Z}}_{2}$ topological order. We examine the two original constructions to measure the topological entropy by combining entropies on plural areas, and we observe that in the large-area limit they both approach the value expected for ${\mathbb{Z}}_{2}$ topological order. We also consider the entanglement entropy on a topologically nontrivial ``zigzag'' area and propose to use it as another way to measure the topological entropy.

arXiv:cond-mat/0612227Physical Review BJun 5, 2007146 citations

Quantum Dimer Model: Phase Diagrams

Garry Goldstein, Claudio Chamon, Claudio Castelnovo

Bulletin of the American Physical SocietyMar 14, 20160 citations

Topological Quantum Many-Body Scars in Quantum Dimer Models

Alexander Seidel, Julia Wildeboer, Anne E. B. Nielsen +1 more

Bulletin of the American Physical SocietyMar 4, 20200 citations

Spontaneous Symmetry Breakings in Z2 Gauge Theories for Doped Quantum Dimer and Eight-Vertex Models

Ikuo Ichinose, Daisuke Yoshioka

Behavior of doped fermions in Z2 gauge theories for the quantum dimer and eight-vertex models is studied. Fermions carry charge and spin degrees of freedom. In the confinement phase of the Z2 gauge theories, these internal symmetries are spontaneously broken and a superconducting or Neél state appears. On the other hand in the deconfinement-topologically-ordered state, all symmetries are respected. From the view point of the quantum dimer and eight-vertex models, this result indicates interplay of the phase structure of the doped fermions and background configuration of the dimer or the eight-vertex groundstate. At the quantum phase transitions in these systems, structure of the doped-fermions groundstate and also that of the background dimer or eight-vertex groundstate both change. Translational symmetry breaking induces a superconducting or antiferromagnetic state of the doped fermions. 1Behavior of doped fermions in Z2 gauge theories for the quantum dimer and eight-vertex models is studied. Fermions carry charge and spin degrees of freedom. In the confinement phase of the Z2 gauge theories, these internal symmetries are spontaneously broken and a superconducting or Neél state appears. On the other hand in the deconfinement-topologically-ordered state, all symmetries are respected. From the view point of the quantum dimer and eight-vertex models, this result indicates interplay of the phase structure of the doped fermions and background configuration of the dimer or the eight-vertex groundstate. At the quantum phase transitions in these systems, structure of the doped-fermions groundstate and also that of the background dimer or eight-vertex groundstate both change. Translational symmetry breaking induces a superconducting or antiferromagnetic state of the doped fermions. 1

Jan 1, 20040 citations

Extend of the

\mathbb{Z}_2

-spin liquid phase on the Kagomé-lattice

The

\mathbb{Z}_2

topological phase in the quantum dimer model on the Kagomé-lattice is a candidate for the description of the low-energy physics of the anti-ferromagnetic Heisenberg model on the same lattice. We study the extend of the topological phase by interpolating between the exactly solvable parent Hamiltonian of the topological phase and an effective low-energy description of the Heisenberg model in terms of a quantum-dimer Hamiltonian. Therefore, we perform a perturbative treatment of the low-energy excitations in the topological phase including free and interacting quasi-particles. We find a phase transition out of the topological phase far from the Heisenberg point. The resulting phase is characterized by a spontaneously broken rotational symmetry and a unit cell involving six sites.

{\mathbb{Z}}_{2}

topological order. We examine the two original constructions to measure the topological entropy by combining entropies on plural areas, and we observe that in the large-area limit they both approach the value expected for

{\mathbb{Z}}_{2}

topological order. We also consider the entanglement entropy on a topologically nontrivial ``zigzag'' area and propose to use it as another way to measure the topological entropy.