Phase diagrams of mixed-spin chains with period 4 using the nonlinearσmodel

Abstract

We study mixed quantum spin chains consisting of two kinds of spins with magnitudes, sa and s b . The spins are arrayed as sa-sa-s b -s b in a unit cell and the exchange couplings are accordingly periodic with period 4. The spin Hamiltonian is mapped onto a nonlinear σ model based on the general formula for periodic inhomogeneous spin chains. The gapless condition given by the nonlinear σ model determines boundaries between disordered phases in the space of the exchange parameters. The phase diagram has a rich phase structure characterized by the values of sa and s b . We explain all phases in the singlet-cluster-solid picture which is an extension of the valence-bond-solid picture.

Quantum Phase Transition of a Quantum Mixed Spin Chain by Employing Density Matrix Renormalization Group Method

“…This model is interesting for the valence‐bond‐solid (VBS) [ 33 ] transition [ 34,35 ] in the ground state controlled by the ratio of two alternating coupling strengths , and it is desirable to understand this type of QPT. On the other hand, this model system belongs to a larger class of quantum mixed spin chains which consist unit cells arrayed as s a ‐ s a ‐ s b ‐ s b , [ 17 ] and the special case, where and , can be realized in a novel germanate Cu 2 Fe 2 Ge 4 O 13 . [ 36 ] Moreover in ref.…”

Finite Size Scaling, Fisher Zeroes and Super Yang-Mills

“…We anticipate competing low-temperature VBS dimer gap states from nonlinear sigma model treatment [4], separated via a quantum phase transition at critical anisotropy at α c . We use a Lieb-Schultz-Mattis extension twist-operator on the groundstate ( |Ψ = U |Ψ 0 ) [6], as an exact order parameter for the VBS states to signal this transition,…”

“…We anticipate competing low-temperature VBS dimer gap states from nonlinear sigma model treatment [4], separated via a quantum phase 1…”

“…also known exactly for comparable models such as the 2D Ising model with Brascamp-Kunz boundary value conditions [5]. We compare the FSS of these indicators to evaluate the critical exponents for the VBS transitions, comparing with nonlinear σ-model predictions.The Hamiltonian for the AHFM two-spin chain with spins S a and S b of period-4 is given as,with J aa =J bb =1 and the coupling anisotropy α = J ab /J aa .We anticipate competing low-temperature VBS dimer gap states from nonlinear sigma model treatment [4], separated via a quantum phase 1 …”

“…Leading corrections to the FSS of the zeroes are sa sb sb sa Jab Jbb Jab Jaa Figure 1. Periodic mixed spin cell, [4]. also known exactly for comparable models such as the 2D Ising model with Brascamp-Kunz boundary value conditions [5].…”