Ground-state phase diagram and low-lying excitation spectrum of the one-dimensional S =1 anisotropic Heisenberg antiferromagnetic chain with nearest neighbor and next nearest neighbor interactions are studied by means of an approximate mapping of the original S =1 spin Hamiltonian to the effective fermion Hamiltonian, which describes the dynamics of spin zero defects in antiferromagnetic environments (domain walls in the Néel state). We find that the frustration due to the next nearest neighbor interactions works cooperatively with quantum fluctuation in the Haldane state and stabilizes it. This is naturally explained in terms of the spin zero defect. In addition, we discuss characteristic features of the excitation spectrum in connection with its ground-state properties.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J(F)(1)) and antiferromagnetic (J(A)(1)) nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction (J(F)(2)). In this model frustration is present due to the non-zero J(F)(2). The model with site spin s behaves like a Haldane spin chain, with site spin 2s in the limit of vanishing J(F)(2)and large J(F)(1)/J(A)(1). We show that the exact ground state of the model can be found along a line in the parameter space. For fixed J(F)(1), the phase diagram in the space of J(A)(1)-J(F)(2) is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
We investigate ground-state and low-lying excited states of the S = 1 antiferromagnetic Heisenberg chain with exchange anisotropy, single-ion anisotropy and biquadratic exchange and with free boundary conditions. We present an approximate mapping of the S = 1 model to an effective S = 1/2 chain in an external magnetic field, which can be solved exactly in several limiting cases. We obtain results for the phase diagram, correlation functions and the excitation spectrum. The transition to the Haldane phase is related to the condensation of the lowest soliton modes and the hidden order parameter of the Haldane phase is identified as transverse long-range order in the effective S = 1/2 chain.
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 a ferromagnetic next-nearest-neighbor interaction (J(2)(F)). In this model frustration is present due to the non-zero J(2)(F). The model with site spin s behaves like a Haldane spin chain, with site spin 2s 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. For fixed J(1)(F), the phase diagram in the space of J(1)(A)-J(2)(F) is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
We use bosonization and renormalization group methods to determine the ground-state phase diagram of a one-dimensional frustrated Kondo-Heisenberg system consisting of a one-dimensional spin-
21 Luttinger liquid coupled by a Kondo exchange interaction
JK to a frustrated quantum antiferromagnetic Heisenberg chain, with a nearest-neighbor exchange coupling
J1 and a next-nearest-neighbor (frustrating) exchange interaction
J2. We analyze the interplay of quantum frustration in the antiferromagnetic chain with the Kondo exchange coupling
JK with the Luttinger liquid. We discuss the structure of the phase diagram of this system as a function of the ratios
JK/J1,
J2/J1, and of the parameters of the Luttinger liquid. In particular, we discuss in detail the regimes in which a pair-density-wave state may be realized and its relation with the spin correlations in the frustrated antiferromagnetic chain.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (
J1F) and antiferromagnetic (
J1A) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (
J2F). In this model frustration is induced by the non-zero
J2F and the effect of dimerization is realized by changing the strength of
J1A for a fixed value of
J1F. The model with site spin
s behaves like a Haldane spin chain with site spin 2
s in the limit of vanishing
J2F and large
J1F/J1A. 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
J1A−J2F 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.