A review of the Contractor Renormalization (CORE) method, as a systematic derivation of the low energy effective hamiltonian, is given, with emphasis on its differences and advantages over traditional perturbative (weak/strong links) real space RG. For the low energy physics of the 2D Hubbard model, we derive the plaquette bosons (projected SO(5)) model which connects the microscopic model to phases and phenomenology of high‐Tc cuprates. For the S = 1/2 Pyrochlore and Kagomé antiferromagnets, the effective hamiltonians predict spin‐disordered, lattice symmetry breaking, ground states with a large density of low energy singlets as found by exact diagonalization of small clusters.A review of the Contractor Renormalization (CORE) method, as a systematic derivation of the low energy effective hamiltonian, is given, with emphasis on its differences and advantages over traditional perturbative (weak/strong links) real space RG. For the low energy physics of the 2D Hubbard model, we derive the plaquette bosons (projected SO(5)) model which connects the microscopic model to phases and phenomenology of high‐Tc cuprates. For the S = 1/2 Pyrochlore and Kagomé antiferromagnets, the effective hamiltonians predict spin‐disordered, lattice symmetry breaking, ground states with a large density of low energy singlets as found by exact diagonalization of small clusters.

arXiv:cond-mat/0510738AIP conference proceedingsJan 1, 20062 citations

Quantum Perfect State Transfer in a 2D Lattice

Sarah Post

Acta Applicandae MathematicaeJun 17, 201412 citations

Quantum Lattice Models for Low-Dimensional Systems

Marco Vekić

Jan 1, 19940 citations

Ground states of quasi-two-dimensional correlated systems via energy expansion

Sam Mardazad, Nicolas Laflorencie, Johannes Motruk +1 more

We introduce a generic method for computing groundstates that is applicable to a wide range of spatially anisotropic 2D many-body quantum systems. By representing the 2D system using a low-energy 1D basis set, we obtain an effective 1D Hamiltonian that only has quasilocal interactions, at the price of a large local Hilbert space. We apply our new method to three specific 2D systems of weakly coupled chains: hardcore bosons, a spin- 1 / 2 Heisenberg, and spinful fermions with repulsive interactions. In particular, we showcase a nontrivial application of the energy expansion framework, to the anisotropic triangular Heisenberg lattice, a highly challenging model related to 2D spin liquids. Treating lattices of unprecedented size, we provide evidence for the existence of a quasi-1D gapless spin liquid state in this system. We also demonstrate the energy expansion framework to perform well where external validation is possible. For the fermionic benchmark in particular, we showcase the energy expansion framework's ability to provide results of comparable quality at a small fraction of the resources required for previous computational efforts.We introduce a generic method for computing groundstates that is applicable to a wide range of spatially anisotropic 2D many-body quantum systems. By representing the 2D system using a low-energy 1D basis set, we obtain an effective 1D Hamiltonian that only has quasilocal interactions, at the price of a large local Hilbert space. We apply our new method to three specific 2D systems of weakly coupled chains: hardcore bosons, a spin- 1 / 2 Heisenberg, and spinful fermions with repulsive interactions. In particular, we showcase a nontrivial application of the energy expansion framework, to the anisotropic triangular Heisenberg lattice, a highly challenging model related to 2D spin liquids. Treating lattices of unprecedented size, we provide evidence for the existence of a quasi-1D gapless spin liquid state in this system. We also demonstrate the energy expansion framework to perform well where external validation is possible. For the fermionic benchmark in particular, we showcase the energy expansion framework's ability to provide results of comparable quality at a small fraction of the resources required for previous computational efforts.

arXiv:2503.22014Physical review. B./Physical review. BNov 25, 20250 citations

State Transfer Hamiltonians in Photonic Lattices

Matthieu Bellec, Georgios M. Nikolopoulos, Stelios Tzortzakis

Springer eBooksAug 21, 20131 citation

Quantum 2‐body Hamiltonian for topological color codes

Héctor Bombín, M. Kargarian, M.A. Martin‐Delgado

Abstract We introduce a two‐body quantum Hamiltonian model with spins‐ ${1 \over 2}$ located on the vertices of a 2D spatial lattice. The model exhibits an exact topological degeneracy in all coupling regimes. This is a remarkable non‐perturbative effect. The model has a Z2× Z2 gauge group symmetry and string‐net integrals of motion. There exists a gapped phase in which the low‐energy sector reproduces an effective topological color code model. High energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. All these, and more, are new features not present in honeycomb lattice models like Kitaev model.Abstract We introduce a two‐body quantum Hamiltonian model with spins‐${1 \over 2}$ located on the vertices of a 2D spatial lattice. The model exhibits an exact topological degeneracy in all coupling regimes. This is a remarkable non‐perturbative effect. The model has a Z2× Z2 gauge group symmetry and string‐net integrals of motion. There exists a gapped phase in which the low‐energy sector reproduces an effective topological color code model. High energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. All these, and more, are new features not present in honeycomb lattice models like Kitaev model.

arXiv:0907.0948Fortschritte der PhysikOct 12, 20096 citations

Abstract We introduce a two‐body quantum Hamiltonian model with spins‐

{1 \over 2}

located on the vertices of a 2D spatial lattice. The model exhibits an exact topological degeneracy in all coupling regimes. This is a remarkable non‐perturbative effect. The model has a Z2× Z2 gauge group symmetry and string‐net integrals of motion. There exists a gapped phase in which the low‐energy sector reproduces an effective topological color code model. High energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. All these, and more, are new features not present in honeycomb lattice models like Kitaev model.