arXiv:1907.00530 · Physical review. B./Physical review. B

Characterization of localized effective spins in gapped quantum spin chains

Hayate Nakano, Seiji Miyashita

Published Nov 4, 2019• 0 citations

Abstract

We study properties of localized effective spins induced in gapped quantum spin chains by local inhomogeneities of the lattice. As a prototype, we study effective spins induced in an impunity sites doped AKLT model by constructing the exact ground state in a matrix product state (MPS) form. We characterize their responses to external fields by studying an extended Zeeman interaction. We also study the antiferromagnetic bond-alternating Heisenberg chain with defect structures. For this model, an MPS representation similar to that for the AKLT model, ``a uniform MPS with windows,'' is constructed, and it gives a good approximation of the ground state. We discuss the trade-off relation between the window length and the precision of the MPS ansatz. The effective exchange interaction between the induced spins is also investigated by using this representation.

DOI: 10.1103/physrevb.100.195105

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arXiv:1907.00530 · Physical review. B./Physical review. B

Characterization of localized effective spins in gapped quantum spin chains

Hayate Nakano, Seiji Miyashita

Published Nov 4, 2019• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.100.195105

Related papers

Local magnetic structures induced by inhomogeneities of the lattice in S=12 bond-alternating chains and their response to a time-dependent magnetic field with noise

Masamichi Nishino, Hiroaki Onishi, Kizashi Yamaguchi +1 more

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We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic ( $J_1^F$ ) and antiferromagnetic ( $J_1^A$ ) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction ( $J_2^F$ ). In this model frustration is induced by the non-zero $J_2^F$ and the effect of dimerization is realized by changing the strength of $J_1^A$ for a fixed value of $J_1^F$ . The model with site spin $s$ behaves like a Haldane spin chain with site spin 2 $s$ in the limit of vanishing $J_2^F$ and large $J_1^F/J_1^A$ . We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of $J_1^A-J_2^F$ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic ($J_1^F$) and antiferromagnetic ($J_1^A$) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction ($J_2^F$). In this model frustration is induced by the non-zero $J_2^F$ and the effect of dimerization is realized by changing the strength of $J_1^A$ for a fixed value of $J_1^F$. The model with site spin $s$ behaves like a Haldane spin chain with site spin 2$s$ in the limit of vanishing $J_2^F$ and large $J_1^F/J_1^A$. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of $J_1^A-J_2^F$ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.

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Masamichi Nishino, Hiroaki Onishi, Pascal Roos +2 more

We study the magnetic properties of $S=1/2$ antiferromagnetic Heisenberg chains with inhomogeneity of interaction. Using a quantum Monte Carlo method and an exact diagonalization method, we study the bond-impurity effect in the uniform $S=1/2$ chain. Here ``bond impurity'' means a bond with a strength different from those in the bulk. In particular, by calculating the local magnetization, the local susceptibility, and the local field susceptibility, the temperature dependence of local magnetic structures induced by bond impurities is investigated. We also investigate the force acting between bond impurities and find that the force is attractive.We study the magnetic properties of $S=1/2$ antiferromagnetic Heisenberg chains with inhomogeneity of interaction. Using a quantum Monte Carlo method and an exact diagonalization method, we study the bond-impurity effect in the uniform $S=1/2$ chain. Here ``bond impurity'' means a bond with a strength different from those in the bulk. In particular, by calculating the local magnetization, the local susceptibility, and the local field susceptibility, the temperature dependence of local magnetic structures induced by bond impurities is investigated. We also investigate the force acting between bond impurities and find that the force is attractive.

arXiv:cond-mat/9906426Physical review. B, Condensed matterFeb 1, 200025 citations

We study the effect of inhomogeneities of the lattice in the

S=1/2

bond-alternating chain by using a quantum Monte Carlo method and an exact diagonalization method. We adopt a defect in the alternating order as the inhomogeneity and we call it ``bond impurity.'' Local magnetic structures induced by the bond impurities are investigated both in the ground state and at very low temperatures. The local magnetic structure can be looked on as an effective

S=1/2

spin and the weakness of the interaction between the local structures causes the quasidegenerate states in the low energy. We also investigate the force acting between bond impurities and find that the force is generally attractive. We also study the dynamical property of the local magnetic structure. While the local magnetic structure behaves as an isolated

S=1/2

spin in the response to a time-dependent uniform field, it is found to be robust against the effect of noise applied at each site individually in the sweeping field.

{n}_{L}

and

{n}_{R}

, that can bind to the left and right edges of the finite chains serve as indices of the particular phase a model belongs to. All these ground states, which we call product vacua with boundary states (PVBS), can be described as matrix product states (MPS). We present a curve of gapped Hamiltonians connecting the Affleck-Kennedy-Lieb-Tasaki (AKLT) model to its representative PVBS model, which has indices

{n}_{L}={n}_{R}=1

. We also present examples with

{n}_{L}={n}_{R}=J

, for any integer $J\ensuremath{\ge}1$, that are related to a recently introduced class of

\text{SO}(2J+1)

-invariant quantum spin chains.

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (

J_1^F

) and antiferromagnetic (

J_1^A

) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (

J_2^F

). In this model frustration is induced by the non-zero

J_2^F

and the effect of dimerization is realized by changing the strength of

J_1^A

for a fixed value of

J_1^F

. The model with site spin

s

behaves like a Haldane spin chain with site spin 2

s

in the limit of vanishing

J_2^F

and large

J_1^F/J_1^A

. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of

J_1^A-J_2^F

is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.

We study the magnetic properties of

S=1/2

antiferromagnetic Heisenberg chains with inhomogeneity of interaction. Using a quantum Monte Carlo method and an exact diagonalization method, we study the bond-impurity effect in the uniform

S=1/2

chain. Here ``bond impurity'' means a bond with a strength different from those in the bulk. In particular, by calculating the local magnetization, the local susceptibility, and the local field susceptibility, the temperature dependence of local magnetic structures induced by bond impurities is investigated. We also investigate the force acting between bond impurities and find that the force is attractive.