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Quantum State Transfer in Spin-1 Chains: Uncovering the Magnetic Order

Oriol Romero‐Isart, K. Eckert, Anna Sanpera

Published Oct 24, 2006• 0 citations
OpenAlex

Abstract

We study the bilinear-biquadratic Heisenberg S=1 spin chain as a quantum channel for transmitting a quantum state. By characterizing such a quantum wire for the whole phase diagram, we find that transport properties reflect the underlying magnetic order present in the ground state. In particular, we identify points in the critical and the dimer phase where transport is very efficient and find a significant reduction of the channel fidelity inside the conjectured spin-nematic region.

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We study the bilinear-biquadratic Heisenberg S=1 spin chain as a quantum channel for transmitting a quantum state. By characterizing such a quantum wire for the whole phase diagram, we find that transport properties reflect the underlying magnetic order present in the ground state. In particular, we identify points in the critical and the dimer phase where transport is very efficient and find a significant reduction of the channel fidelity inside the conjectured spin-nematic region.
We study the transfer of a quantum state through a Heisenberg spin-1 chain prepared in its ground state. We characterize the efficiency of the transfer via the fidelity of retrieving an arbitrarily prepared state and also via the transfer of quantum entanglement. The Heisenberg spin-1 chain has a very rich quantum phase diagram. We show that the boundaries of the different quantum phases are reflected in sharp variations of the transfer efficiency. In the vicinity of the border between the dimer and the ferromagnetic phase (in the conjectured spin-nematic region), we find strong indications for a qualitative change of the excitation spectrum. Moreover, we identify two regions of the phase diagram that give rise to particularly high transfer efficiency; the channel might be nonclassical even for chains of arbitrary length, in contrast to spin-1∕21∕21∕2 chains.
Higher-spin materials can host exotic quantum phases with no counterparts in familiar spin-\textonehalf{} systems. Using density matrix renormalization group calculations, the authors chart here the phase diagram of a spin-1 bilinear-biquadratic-Kitaev chain and reveal two Kitaev-driven phases. A Kitaev nematic phase emerges from a delicate biquadratic-dimer background through an Ising quantum critical point, which further evolves into a Kitaev dimer phase that spontaneously breaks screw symmetry and crystallizes into a gapped order of alternating \ensuremath{\mathbb{Z}}2{}_{2}2​ bond parities.
Nematic order is an exotic property observed in several strongly correlated systems, such as iron-based superconductors. Using large-scale density matrix renormalization group (DMRG) techniques, we study at zero temperature the nematic spin liquid that competes with spin dipolar and quadrupolar orders. We use these nematic orders to characterize different quantum phases and quantum phase transitions. More specifically, we study a spin-1 bilinear-biquadratic Heisenberg model on the square lattice with couplings beyond nearest neighbors. We focus on parameter regions around the highly symmetric SU(3)SU(3)SU(3) point where the bilinear and biquadratic interactions are equal. With growing further-neighbor biquadratic interactions, we identify different spin dipolar and quadrupolar orders. We find that the DMRG results for cylindrical geometries correctly detect nematicity in different quantum states and accurately characterize the quantum phase transitions among them. Therefore, spin-driven nematicity, here defined as the spontaneous breaking of the lattice invariance under a ${90}^{\ensuremath{\circ}}$ rotation, is an order parameter which can be studied directly in DMRG calculations in two dimensions in different quantum states.