We show that a quantum spin circulator, a nonreciprocal device that routes spin currents without any charge transport, can be achieved in Y junctions of identical spin- $1/2$ Heisenberg chains coupled by a chiral three-spin interaction. Using bosonization, boundary conformal field theory, and density matrix renormalization group simulations, we find that a chiral fixed point with maximally asymmetric spin conductance arises at a critical point separating a regime of disconnected chains from a spin-only version of the three-channel Kondo effect. We argue that networks of spin-chain Y junctions provide a controllable approach to construct long-sought chiral spin-liquid phases.We show that a quantum spin circulator, a nonreciprocal device that routes spin currents without any charge transport, can be achieved in Y junctions of identical spin-$1/2$ Heisenberg chains coupled by a chiral three-spin interaction. Using bosonization, boundary conformal field theory, and density matrix renormalization group simulations, we find that a chiral fixed point with maximally asymmetric spin conductance arises at a critical point separating a regime of disconnected chains from a spin-only version of the three-channel Kondo effect. We argue that networks of spin-chain Y junctions provide a controllable approach to construct long-sought chiral spin-liquid phases.

arXiv:1801.04594Physical review. B./Physical review. BJun 11, 201813 citations

Critical Properties of Spin Chains

Satoshi Takada

Springer series in solid-state sciencesJan 1, 19873 citations

Novel massive ground states of spin chains in a magnetic field

Kiyohito Totsuka

The European Physical Journal BOct 1, 199828 citations

Hierarchy of exactly solvable spin- 12 chains with so(N)1 critical points

Ville Lahtinen, Teresia Månsson, Eddy Ardonne

We construct a hierarchy of exactly solvable spin-1/2 chains with $so{(N)}_{1}$ critical points. Our construction is based on the framework of condensate-induced transitions between topological phases. We employ this framework to construct a Hamiltonian term that couples $N$ transverse field Ising chains such that the resulting theory is critical and described by the $so{(N)}_{1}$ conformal field theory. By employing spin duality transformations, we then cast these spin chains for arbitrary $N$ into translationally invariant forms that all allow exact solution by the means of a Jordan-Wigner transformation. For odd $N$ our models generalize the phase diagram of the transverse field Ising chain, the simplest model in our hierarchy. For even $N$ the models can be viewed as longer ranger generalizations of the $XY$ chain, the next model in the hierarchy. We also demonstrate that our method of constructing spin chains with given critical points goes beyond exactly solvable models. Applying the same strategy to the Blume-Capel model, a spin-1 generalization of the Ising chain in a generic magnetic field, we construct another critical spin-1 chain with the predicted conformal field theory (CFT) describing the criticality.We construct a hierarchy of exactly solvable spin-1/2 chains with $so{(N)}_{1}$ critical points. Our construction is based on the framework of condensate-induced transitions between topological phases. We employ this framework to construct a Hamiltonian term that couples $N$ transverse field Ising chains such that the resulting theory is critical and described by the $so{(N)}_{1}$ conformal field theory. By employing spin duality transformations, we then cast these spin chains for arbitrary $N$ into translationally invariant forms that all allow exact solution by the means of a Jordan-Wigner transformation. For odd $N$ our models generalize the phase diagram of the transverse field Ising chain, the simplest model in our hierarchy. For even $N$ the models can be viewed as longer ranger generalizations of the $XY$ chain, the next model in the hierarchy. We also demonstrate that our method of constructing spin chains with given critical points goes beyond exactly solvable models. Applying the same strategy to the Blume-Capel model, a spin-1 generalization of the Ising chain in a generic magnetic field, we construct another critical spin-1 chain with the predicted conformal field theory (CFT) describing the criticality.

arXiv:1310.1876Physical Review BJan 10, 201414 citations

Ordering and Criticality in Spin-1 Chains

Rajiv R. P. Singh, Martin P. Gelfand

Physical Review LettersJan 2, 19892 citations

Classification of quantum critical states of integrable antiferromagnetic spin chains and their correspondent two-dimensional topological phases

Zheng-Xin Liu, Zhang, Guang-Ming

We examine the effective field theory of the Bethe ansatz integrable Heisenberg antiferromagnetic spin chains. It shows that the quantum critical theories for the integer spin-S chains should be characterized by the SO(3)level-S Wess-Zumino-Witten model, and classified by the third cohomology group $H^{3}(SO(3),Z)=Z$ . Depending on the parity of spin S, this integer classification is further divided into two distinct universality classes, which are associated with two completely different conformal field theories: the even-S chains have gapless bosonic excitations and the odd-S chains have both bosonic and fermionic excitations. We further show that these two classes of critical states correspond to the boundary states of two distinct topological phases in two dimension, which can be described by two-dimensional doubled SO(3) topological Chern-Simons theory and topological spin theory, respectively.We examine the effective field theory of the Bethe ansatz integrable Heisenberg antiferromagnetic spin chains. It shows that the quantum critical theories for the integer spin-S chains should be characterized by the SO(3)level-S Wess-Zumino-Witten model, and classified by the third cohomology group $H^{3}(SO(3),Z)=Z$. Depending on the parity of spin S, this integer classification is further divided into two distinct universality classes, which are associated with two completely different conformal field theories: the even-S chains have gapless bosonic excitations and the odd-S chains have both bosonic and fermionic excitations. We further show that these two classes of critical states correspond to the boundary states of two distinct topological phases in two dimension, which can be described by two-dimensional doubled SO(3) topological Chern-Simons theory and topological spin theory, respectively.

arXiv:1211.5421Nov 23, 20120 citations

We show that a quantum spin circulator, a nonreciprocal device that routes spin currents without any charge transport, can be achieved in Y junctions of identical spin-

1/2

Heisenberg chains coupled by a chiral three-spin interaction. Using bosonization, boundary conformal field theory, and density matrix renormalization group simulations, we find that a chiral fixed point with maximally asymmetric spin conductance arises at a critical point separating a regime of disconnected chains from a spin-only version of the three-channel Kondo effect. We argue that networks of spin-chain Y junctions provide a controllable approach to construct long-sought chiral spin-liquid phases.

We construct a hierarchy of exactly solvable spin-1/2 chains with

so{(N)}_{1}

critical points. Our construction is based on the framework of condensate-induced transitions between topological phases. We employ this framework to construct a Hamiltonian term that couples

N

transverse field Ising chains such that the resulting theory is critical and described by the

so{(N)}_{1}

conformal field theory. By employing spin duality transformations, we then cast these spin chains for arbitrary

N

into translationally invariant forms that all allow exact solution by the means of a Jordan-Wigner transformation. For odd

N

our models generalize the phase diagram of the transverse field Ising chain, the simplest model in our hierarchy. For even

N

the models can be viewed as longer ranger generalizations of the

XY

chain, the next model in the hierarchy. We also demonstrate that our method of constructing spin chains with given critical points goes beyond exactly solvable models. Applying the same strategy to the Blume-Capel model, a spin-1 generalization of the Ising chain in a generic magnetic field, we construct another critical spin-1 chain with the predicted conformal field theory (CFT) describing the criticality.

H^{3}(SO(3),Z)=Z

. Depending on the parity of spin S, this integer classification is further divided into two distinct universality classes, which are associated with two completely different conformal field theories: the even-S chains have gapless bosonic excitations and the odd-S chains have both bosonic and fermionic excitations. We further show that these two classes of critical states correspond to the boundary states of two distinct topological phases in two dimension, which can be described by two-dimensional doubled SO(3) topological Chern-Simons theory and topological spin theory, respectively.