We consider a chain of spinful fermions with nearest neighbor hopping in the presence of a $XY$ antiferromagnetic interaction. The $XY$ term is mapped onto a Kitaev chain at half-filling such that displays a bosonic zero mode topologically protected and long-range order. As the strength of the hopping amplitude is changed, the system undergoes a quantum phase transition from the topological non-trivial to the trivial phase. We apply the finite-size scaling method to determinate the phase diagram of the model.We consider a chain of spinful fermions with nearest neighbor hopping in the presence of a $XY$ antiferromagnetic interaction. The $XY$ term is mapped onto a Kitaev chain at half-filling such that displays a bosonic zero mode topologically protected and long-range order. As the strength of the hopping amplitude is changed, the system undergoes a quantum phase transition from the topological non-trivial to the trivial phase. We apply the finite-size scaling method to determinate the phase diagram of the model.

arXiv:2105.04326May 10, 20210 citations

PHASE TRANSITIONS IN QUANTUM SPIN CHAINS

Jenő Sólyom

WORLD SCIENTIFIC eBooksApr 1, 19920 citations

Entanglement in Interacting Majorana Chains and Transitions of von Neumann Algebras

Pablo Basteiro, Giuseppe Di Giulio, Johanna Erdmenger B +1 more

We consider Majorana lattices with two-site interactions consisting of a general function of the fermion bilinear. The models are exactly solvable in the limit of a large number of on-site fermions. The four-site chain exhibits a quantum phase transition controlled by the hopping parameters and manifests itself in a discontinuous entanglement entropy, obtained by constraining the one-sided modular Hamiltonian. Inspired by recent work within the AdS/CFT correspondence, we identify transitions between types of von Neumann operator algebras throughout the phase diagram. We find transitions of the form II_{1}↔III↔I_{∞} that reduce to II_{1}↔I_{∞} in the strongly interacting limit, where they connect nonfactorized and factorized ground states. Our results provide novel realizations of such transitions in a controlled many-body model.We consider Majorana lattices with two-site interactions consisting of a general function of the fermion bilinear. The models are exactly solvable in the limit of a large number of on-site fermions. The four-site chain exhibits a quantum phase transition controlled by the hopping parameters and manifests itself in a discontinuous entanglement entropy, obtained by constraining the one-sided modular Hamiltonian. Inspired by recent work within the AdS/CFT correspondence, we identify transitions between types of von Neumann operator algebras throughout the phase diagram. We find transitions of the form II_{1}↔III↔I_{∞} that reduce to II_{1}↔I_{∞} in the strongly interacting limit, where they connect nonfactorized and factorized ground states. Our results provide novel realizations of such transitions in a controlled many-body model.

arXiv:2401.04764Physical Review LettersApr 16, 20247 citations

Quantum Critical Phenomena in an $O(4)$ Fermion ChainQuantum Critical Phenomena in an $O(4)$ Fermion Chain

Hanqing Liu, Shailesh Chandrasekharan A, Ribhu K. Kaul

We construct a fermionic lattice model containing interacting spin- $\frac{1}{2}$ fermions with an $O(4)$ symmetry. In addition the model contains a $\mathbb{Z}_2$ chiral symmetry which prevents a fermion mass term. Our model is motivated by the ability to study its physics using the meron-cluster algorithm. By adding a strong repulsive Hubbard interaction $U$ , we can transform it into the regular Heisenberg anti-ferromagnet. While we can study our model in any dimension, as a first project we study it in one spatial dimension. We discover that our model at $U=0$ can be described as a lattice-regularized 2-flavor Gross-Neveu model, where fermions become massive since the $\mathbb{Z}_2$ chiral symmetry of the model is spontaneously broken. We show numerically that the theory remains massive when $U$ is small. At large values of $U$ the model is equivalent to the isotropic spin-half anti-ferromagnetic chain, which is massless for topological reasons. This implies that our model has a quantum phase transition from a $\mathbb{Z}_2$ broken massive phase to a topologically massless phase as we increase $U$ . We present results obtained from our quantum Monte Carlo method near this phase transition.We construct a fermionic lattice model containing interacting spin-$\frac{1}{2}$ fermions with an $O(4)$ symmetry. In addition the model contains a $\mathbb{Z}_2$ chiral symmetry which prevents a fermion mass term. Our model is motivated by the ability to study its physics using the meron-cluster algorithm. By adding a strong repulsive Hubbard interaction $U$, we can transform it into the regular Heisenberg anti-ferromagnet. While we can study our model in any dimension, as a first project we study it in one spatial dimension. We discover that our model at $U=0$ can be described as a lattice-regularized 2-flavor Gross-Neveu model, where fermions become massive since the $\mathbb{Z}_2$ chiral symmetry of the model is spontaneously broken. We show numerically that the theory remains massive when $U$ is small. At large values of $U$ the model is equivalent to the isotropic spin-half anti-ferromagnetic chain, which is massless for topological reasons. This implies that our model has a quantum phase transition from a $\mathbb{Z}_2$ broken massive phase to a topologically massless phase as we increase $U$. We present results obtained from our quantum Monte Carlo method near this phase transition.

arXiv:1912.11237International Symposium on Lattice Field Theory (LATTICE)Jan 4, 20202 citations

Phase transition in a fermion model

秀典宮田

Jan 1, 19820 citations

A Spin

1/2

Fermions Chain with

XY

Interaction

We consider a chain of spinful fermions with nearest neighbor hopping in the presence of a

XY

antiferromagnetic interaction. The

XY

term is mapped onto a Kitaev chain at half-filling such that displays a bosonic zero mode topologically protected and long-range order. As the strength of the hopping amplitude is changed, the system undergoes a quantum phase transition from the topological non-trivial to the trivial phase. We apply the finite-size scaling method to determinate the phase diagram of the model.

Quantum Critical Phenomena in an

O(4)

Fermion Chain

We construct a fermionic lattice model containing interacting spin-

\frac{1}{2}

fermions with an

O(4)

symmetry. In addition the model contains a

\mathbb{Z}_2

chiral symmetry which prevents a fermion mass term. Our model is motivated by the ability to study its physics using the meron-cluster algorithm. By adding a strong repulsive Hubbard interaction

U

, we can transform it into the regular Heisenberg anti-ferromagnet. While we can study our model in any dimension, as a first project we study it in one spatial dimension. We discover that our model at

U=0

can be described as a lattice-regularized 2-flavor Gross-Neveu model, where fermions become massive since the

\mathbb{Z}_2

chiral symmetry of the model is spontaneously broken. We show numerically that the theory remains massive when

U

is small. At large values of

U

the model is equivalent to the isotropic spin-half anti-ferromagnetic chain, which is massless for topological reasons. This implies that our model has a quantum phase transition from a

\mathbb{Z}_2

broken massive phase to a topologically massless phase as we increase

U

. We present results obtained from our quantum Monte Carlo method near this phase transition.