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arXiv:1809.00743 · Physical review. B./Physical review. B

Inducing critical phenomena in spin chains through sparse alternating fields

Marco Cerezo, R. Rossignoli, N. Canosa, Carlos Alberto Lamas

Published Jan 9, 2019• 3 citations
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Abstract

We analyze the phase diagram of the exact ground state (GS) of spin-$s$ chains with ferromagnetic XXZ couplings under $n$-alternating field configurations, i.e., sparse alternating fields having nodes at $n\ensuremath{-}1$ contiguous sites. It is shown that such systems can exhibit a nontrivial magnetic behavior, which can differ significantly from that of the standard $(n=1)$ alternating case and enable mechanisms for controlling their magnetic and entanglement properties. The boundary in field space of the fully aligned phase can be determined analytically $\ensuremath{\forall}\phantom{\rule{0.28em}{0ex}}n$, and shows that it becomes reachable only above a threshold value of the coupling anisotropy ${J}_{z}/J$, which depends on $n$ but is independent of the system size. Below this value, the maximum attainable magnetization becomes much smaller. We then show that the GS can exhibit significant magnetization plateaus, persistent for large systems, at which the magnetization per site $m$ obeys the quantization rule $2n(s\ensuremath{-}m)=\text{integer}$, consistent with the Oshikawa, Yamanaka, and Affleck criterion. We also identify the emergence of field-induced spin polymerization, which explains the presence of such plateaus. Entanglement and field-induced frustration effects are also analyzed.

DOI
10.1103/physrevb.99.014409

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We analyze the phase diagram of the exact ground state (GS) of spin-sss chains with ferromagnetic XXZ couplings under nnn-alternating field configurations, i.e., sparse alternating fields having nodes at n\ensuremath−1n\ensuremath{-}1n\ensuremath−1 contiguous sites. It is shown that such systems can exhibit a nontrivial magnetic behavior, which can differ significantly from that of the standard (n=1)(n=1)(n=1) alternating case and enable mechanisms for controlling their magnetic and entanglement properties. The boundary in field space of the fully aligned phase can be determined analytically \ensuremath∀n\ensuremath{\forall}\phantom{\rule{0.28em}{0ex}}n\ensuremath∀n, and shows that it becomes reachable only above a threshold value of the coupling anisotropy Jz/J{J}_{z}/JJz​/J, which depends on nnn but is independent of the system size. Below this value, the maximum attainable magnetization becomes much smaller. We then show that the GS can exhibit significant magnetization plateaus, persistent for large systems, at which the magnetization per site mmm obeys the quantization rule 2n(s\ensuremath−m)=integer2n(s\ensuremath{-}m)=\text{integer}2n(s\ensuremath−m)=integer, consistent with the Oshikawa, Yamanaka, and Affleck criterion. We also identify the emergence of field-induced spin polymerization, which explains the presence of such plateaus. Entanglement and field-induced frustration effects are also analyzed.
We analyze ground state (GS) factorization in general arrays of spins s_{i} with XXZ couplings immersed in nonuniform fields. It is shown that an exceptionally degenerate set of completely separable symmetry-breaking GSs can arise for a wide range of field configurations, at a quantum critical point where all GS magnetization plateaus merge. Such configurations include alternating fields as well as zero-bulk field solutions with edge fields only and intermediate solutions with zero field at specific sites, valid for d-dimensional arrays. The definite magnetization-projected GSs at factorization can be analytically determined and depend only on the exchange anisotropies, exhibiting critical entanglement properties. We also show that some factorization-compatible field configurations may result in field-induced frustration and nontrivial behavior at strong fields.
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 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 study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J1FJ_1^FJ1F​) and antiferromagnetic (J1AJ_1^AJ1A​) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (J2FJ_2^FJ2F​). In this model frustration is induced by the non-zero J2FJ_2^FJ2F​ and the effect of dimerization is realized by changing the strength of J1AJ_1^AJ1A​ for a fixed value of J1FJ_1^FJ1F​. The model with site spin sss behaves like a Haldane spin chain with site spin 2sss in the limit of vanishing J2FJ_2^FJ2F​ and large J1F/J1AJ_1^F/J_1^AJ1F​/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−J2FJ_1^A-J_2^FJ1A​−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.
The ground state properties of the high spin Heisenberg chains with alternating single site anisotropy are investigated by means of the numerical exact daigonaization and DMRG method. It is found that the ferrimagnetic state appears between the Haldane phase and period doubled Néel phase for the integer spin chains. On the other hand, the transition from the Tomonaga-Luttinger liquid state into the ferrimagnetic state takes place for the half-odd-integer spin chains. In the ferrimagnetic phase, the spontaneous magnetization varies continuously with the modulation amplitude of the single site anisotropy. Eventually, the magnetization is locked to fractional values of the saturated magnetization. These fractional values satisfy the Oshikawa-Yamanaka-Affleck condition. The local spin profile is calculated to reveal the physical nature of each state. In contrast to the case of frustration induced ferrimagnetism, no incommensurate magnetic superstructure is found.
The ground state properties of the high spin Heisenberg chains with alternating single site anisotropy are investigated by means of the numerical exact daigonaization and DMRG method.It is found that the ferrimagnetic state appears between the Haldane phase and period doubled Néel phase for the integer spin chains.On the other hand, the transition from the Tomonaga-Luttinger liquid state into the ferrimagnetic state takes place for the half-odd-integer spin chains.In the ferrimagnetic phase, the spontaneous magnetization varies continuously with the modulation amplitude of the single site anisotropy.Eventually, the magnetization is locked to fractional values of the saturated magnetization.These fractional values satisfy the Oshikawa-Yamanaka-Affleck condition.The local spin profile is calculated to reveal the physical nature of each state.In contrast to the case of frustration induced ferrimagnetism, no incommensurate magnetic superstructure is found.