Atomic spin-chain realization of a model for quantum criticality

Abstract

The ability to manipulate single atoms has opened up the door to constructing interesting and useful quantum structures from the ground up 1 . On the one hand, nanoscale arrangements of magnetic atoms are at the heart of future quantum computing and spintronic devices 2,3 ; on the other hand, they can be used as fundamental building blocks for the realization of textbook many-body quantum models 4 , illustrating key concepts such as quantum phase transitions, topological order or frustration as a function of system size. Here, we use low-temperature scanning tunnelling microscopy to construct arrays of magnetic atoms on a surface, designed to behave like spin-1/2 XXZ Heisenberg chains in a transverse field, for which a quantum phase transition from an antiferromagnetic to a paramagnetic phase is predicted in the thermodynamic limit 5. Site-resolved measurements on these finite-size realizations reveal a number of sudden ground state changes when the field approaches the critical value, each corresponding to a new domain wall entering the chains. We observe that these state crossings become closer for longer chains, suggesting the onset of critical behaviour. Our results present opportunities for further studies on quantum behaviour of many-body systems, as a function of their size and structural complexity.Since the birth of quantum mechanics, lattice spin systems 6 have represented a natural starting point for understanding collective quantum dynamics. Today, scanning tunnelling microscopy (STM) techniques allow one to experimentally build and probe realizations of exchange-coupled lattice spins in different geometries [7][8][9] . In linear arrangements, quantum effects are strongest 10 and notions such as quantum phase transitions 11 are most easily understood, the simplest illustration being the Ising model in a transverse field 12,13 . In this work, using STM, we construct finite-size versions of a model in the same universality class, namely the spin-1/2 XXZ chain in a transverse field 5 , which has previously been realized in the bulk material Cs 2 CoCl 4 (refs 14,15). Our set-up allows us to probe the chains with single-spin resolution while tuning an externally applied transverse field through the critical regime.The chains are created by manipulating Co atoms evaporated onto a Cu 2 N/Cu(100) surface (see Methods), which provides efficient decoupling for the magnetic d-shell electrons from the underlying bulk electrons 7 . Employing inelastic electron tunnelling spectroscopy (IETS) 16,17 at sufficiently low temperature (330 mK) allows us to determine the magnetic anisotropy vector of each atom 18 as well as the strength of the exchange coupling between neighbouring atoms 19 . It was previously demonstrated that Co atoms on this surface behave as spin S = 3/2 objects experiencing a strong uniaxial hard-axis anisotropy pointing inplane, perpendicular to the bond with the neighbouring N atoms 20 . As a result, the m z = ±3/2 states split off approximately 5.5 meV above the m z = ±1/2 doublet (see Fig. 1a)...

Field-Induced Magnonic Liquid in the 3D Spin-Dimerized AntiferromagnetSr3Cr2O8Wang1, Quintero-Castro2, Жерлицын3 et al. 2016Phys. Rev. Lett.192801View full textAdd to dashboardCite

“…Due to enhanced quantum fluctuations and reduced dimensionality, the low-dimensional quantum magnets host very often exotic quantum states of matter [1][2][3][4][5][6][7][8][9][10][11][12][13] . Especially for the one-dimensional (1D) spin systems, realization of novel quantum spin states is not only of lively experimental interest [7][8][9][10]12,13 but also a constant focus of theoretical study 1,2,[14][15][16][17] , since quantitative description of the elementary excitations can be provided by rigorous theoretical approaches and precise comparisons between theoretical predictions and experimental results can be made [7][8][9][10]12,13,15 .…”

Nonperturbative effects and indirect exchange interaction between quantum impurities on metallic (111) surfaces

“…[1][2][3] This technique can, for example, uncover spatial profiles of magnetic excitations in artificial one-dimensional spin chains [4][5][6][7] . The surface not only supports the spin centres, but also plays a crucial role in stabilizing magnetic order [8][9][10][11] .…”

Level crossings induced by a longitudinal coupling in the transverse field Ising chain

“…In a recent experiment with chains of Cobalt atoms evaporated onto a Cu 2 N/Cu(100) substrate [10], the presence of level crossings as a function of the external magnetic field has been revealed by scanning tunneling microscopy, which exhibits a specific signature whenever the ground state is degenerate. The relevant effective model for that system is a spin-1/2 XY model in an inplane magnetic field.…”

“…Their detection is much less easy than that of magnetic edge states, and it relies on indirect consequences such as their impact on the local tunneling density of states [7,8], or the presence of two quasi-degenerate low-lying states in open systems. In that respect, it has been suggested to look for situations where the low-lying states cross as a function of an external parameter, for instance the chemical potential, to prove that there are indeed two low-lying states [9].In a recent experiment with chains of Cobalt atoms evaporated onto a Cu 2 N/Cu(100) substrate [10], the presence of level crossings as a function of the external magnetic field has been revealed by scanning tunneling microscopy, which exhibits a specific signature whenever the ground state is degenerate. The relevant effective model for that system is a spin-1/2 XY model in an inplane magnetic field.…”