Full characterization of the quantum linear‐zigzag transition in atomic chains

Abstract

A string of repulsively interacting particles exhibits a phase transition to a zigzag structure, by reducing the transverse trap potential or the interparticle distance. Based on the emergent symmetry Z 2 it has been argued that this instability is a quantum phase transition, which can be mapped to an Ising model in transverse field. An extensive Density Matrix Renormalization Group analysis is performed, resulting in an high-precision evaluation of the critical exponents and of the central charge of the system, confirming that the quantum linear-zigzag transition belongs to the critical Ising model universality class. Quantum corrections to the classical phase diagram are computed, and the range of experimental parameters where quantum effects play a role is provided. These results show that structural instabilities of one-dimensional interacting atomic arrays can simulate quantum critical phenomena typical of ferromagnetic systems.Quantum field theories full characterisation heavily depends on simulation methods as they are in general not exactly analytically solvable [1]. One prominent example is provided by the φ 4 type of models [2][3][4][5], which are encountered in solid state and high-energy models and whose predictions need verification [6,7]. These verifications have been partly performed via classical simulations [8][9][10], however it would also be desirable to have a controllable quantum system whose dynamics reproduces that of the model of interest, that is a quantum simulator [11][12][13][14][15][16]. The zigzag instability of interacting atomic chains is a realization of φ 4 model which can be realized in laboratory [17][18][19][20]. This transition is sketched in Fig. 1 and has been observed in systems of singly-charged ions confined by external potentials, where the instability is controlled either by lowering the transverse potential or the linear density [21,22]. Due to its universal properties, it can be observed in arrays of other repulsively interacting (quasi) particles [23,24], such as electrons in quantum wires [25], ultracold gases in optical lattices mutually repelling via the dipolar interaction [26,27] or via the off-resonant coupling with a Rydberg excitation [28], or vortices in quantum gases [29]. In these systems ultralow temperatures are typically achieved, so that quantum effects at criticality are dominant. Motivated by the emergent Z 2 symmetry and previous numerical investigations, it has been argued that the linear-zigzag structural instability is a quantum phase transition [23,25], which in 1 + 1 dimensions can be mapped to a Ising model in the transverse field, describing a ferromagnetic transition at zero temperature [7]. However, a mathematical proof or a conclusive numerical evidence of this statement is still unavailable, and thus a precise numerical verification is needed. Indeed ab-initio calculations are essential to

Ab initiocharacterization of the quantum linear-zigzag transition using density matrix renormalization group calculations

“…Secondly, we give a robust and scientifically sound background to the results some of us previously presented in Ref. 52 , as well as expand that work by adding previously unreported comments. Finally, we take a special care in reporting all the numerical expedients we adopt so that all of our results will be fully reproducible.…”

Ion Traps as a testbed of classical and quantum statistical mechanics

“…In their paper [37] they prove by direct numerical simulation that the quantum linear to zig-zag structural phase transition is in the same universal class at the Ising chain thereby corroborating the theoretical prediction of [38]. A first theoretical insight was to concentrate on the small fluctuations regime in which transverse and longitudinal motion are decoupled from each other.…”

“…Beyond its relevance to fundamental physics, this tunable double well potential can also be used to fully characterize the properties of the environmental noise using double well interferometry [36]. Thus the study of the properties of the linear to zigzag phase transition in the quantum regime is a topic of considerable interest to which Silvi et al [37] make a substantial contribution.…”

Non-Markovian Quantum Probes

“…If the transverse confinement is reduced or the density of the ions in the chain is increased, the chain undergoes a structural phase transition to a zigzag structure. The precise nature of the structural linearzigzag phase transition is still unresolved, but there is increasing evidence that it is a quantum phase transition [49], and of the same universality class as the transverse Ising model [50].…”