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arXiv:1801.01445 · Physical Review Letters

Detection of a Disorder-Induced Bose-Einstein Condensate in a Quantum Spin Material at High Magnetic Fields

Anna Yu. Orlova, H. Mayaffre, S. Krämer, Maxime Dupont, Sylvain Capponi, Nicolas Laflorencie, Armando Paduan-Filho, M. Horvatić

Published Oct 25, 2018• 13 citations
arXivHTMLPDF

Abstract

The coupled spin-1 chains material NiCl_{2}-4SC(NH_{2})_{2} (DTN) doped with Br impurities is expected to be a perfect candidate for observing many-body localization at high magnetic field: the so-called "Bose glass," a zero-temperature bosonic fluid, compressible, gapless, incoherent, and short-range correlated. Using nuclear magnetic resonance, we critically address the stability of the Bose glass in doped DTN, and find that it hosts a novel disorder-induced ordered state of matter, where many-body physics leads to an unexpected resurgence of quantum coherence emerging from localized impurity states. An experimental phase diagram of this new "order-from-disorder" phase, established from nuclear magnetic resonance T_{1}^{-1} relaxation rate data in the 13±1% Br-doped DTN, is found to be in excellent agreement with the theoretical prediction from large-scale quantum Monte Carlo simulations.

DOI
10.1103/physrevlett.121.177202

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The coupled spin-1 chains material NiCl_{2}-4SC(NH_{2}){2} (DTN) doped with Br impurities is expected to be a perfect candidate for observing many-body localization at high magnetic field: the so-called "Bose glass," a zero-temperature bosonic fluid, compressible, gapless, incoherent, and short-range correlated. Using nuclear magnetic resonance, we critically address the stability of the Bose glass in doped DTN, and find that it hosts a novel disorder-induced ordered state of matter, where many-body physics leads to an unexpected resurgence of quantum coherence emerging from localized impurity states. An experimental phase diagram of this new "order-from-disorder" phase, established from nuclear magnetic resonance T{1}^{-1} relaxation rate data in the 13±1% Br-doped DTN, is found to be in excellent agreement with the theoretical prediction from large-scale quantum Monte Carlo simulations.
We study the interplay between disorder and interactions for emergent bosonic degrees of freedom induced by an external magnetic field in the Br-doped spin-gapped antiferromagnetic material $\mathrm{Ni}{({\mathrm{Cl}}_{1\ensuremath{-}x}{\mathrm{Br}}_{x})}_{2}\ensuremath{-}4\mathrm{SC}{({\mathrm{NH}}_{2})}_{2}$ (DTNX\mathrm{DTN}XDTNX). Building on nuclear magnetic resonance experiments at high magnetic field [A. Orlova et al., Phys. Rev. Lett. 118, 067203 (2017)], we describe the localization of isolated impurity states, providing a realistic theoretical modeling for DTNX\mathrm{DTN}XDTNX. Going beyond single impurity localization we use quantum Monte Carlo simulations to explore many-body effects from which pairwise effective interactions lead to a (impurity-induced) Bose-Einstein condensation (BEC) revival [M. Dupont, S. Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017)]. We further address the question of the existence of a many-body localized Bose-glass (BG) phase in DTNX\mathrm{DTN}XDTNX, which is found to compete with a series of a new kind of BEC regimes made out of the multi-impurity states. The global magnetic field--temperature phase diagram of DTNX\mathrm{DTN}XDTNX reveals a very rich structure for low impurity concentration, with consecutive disorder-induced BEC minidomes separated by intervening many-body localized BG regimes. Upon increasing the impurity level, multiple mini-BEC phases start to overlap, while intermediate BG regions vanish.
We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate 1/T11/{T}_{1}1/T1​ in random one-dimensional spin chains as a function of the temperature and disorder strength. In the zero temperature limit, the system displays a disorder-induced quantum phase transition between a critical Tomonaga-Luttinger liquid (TLL) phase and a localized Bose glass phase. The 1/T11/{T}_{1}1/T1​ is investigated across this transition using large-scale simulations based on matrix product state techniques. We find that this quantity can detect the transition and probe the value of the dimensionless TLL parameter KKK. We also compute the NMR relaxation rate distributions for each temperature and disorder strength considered. In particular, we discuss the applicability of the stretched exponential fit to the return-to-equilibrium function to extract the 1/T11/{T}_{1}1/T1​ experimentally. The results presented here should provide valuable insights in regards of future NMR experiments in realistic disordered spin compounds.
A quantum particle cannot in general diffuse through a disordered medium because of its wavelike nature, but interacting particles can escape localization by collectively percolating through the system. For bosonic particles this phenomenon corresponds to a quantum transition from a localized insulator phase —the Bose glass— to a superfluid phase, in which particles condense into an extended state. Here, we construct a universal phase diagram of disordered bosons in doped quantum magnets for which bosonic quasiparticles are represented by magnetized states (spin triplets) of the quantum spins, condensing into a magnetically ordered state. The appearance of a Bose glass leads to strong measurable signatures in the onset of superfluidity of the spin-triplet gas, exhibiting a complex crossover from low-temperature quantum percolation to a conventional condensation transition at intermediate temperatures.
We numerically investigate the phase diagram of two-dimensional site-diluted coupled dimer systems in an external magnetic field. We show that this phase diagram is characterized by the presence of an extended Bose glass, not accessible to mean-field approximation, and stemming from the localization of two distinct species of bosonic quasiparticles appearing in the ground state. On the one hand, nonmagnetic impurities doped into the dimer-singlet phase of a weakly coupled dimer system are known to free up local magnetic moments. The deviations of these local moments from full polarization along the field can be mapped onto a gas of bosonic quasiparticles, which undergo condensation in zero and very weak magnetic fields, corresponding to transverse long-range antiferromagnetic order. An increasing magnetic field lowers the density of such quasiparticles to a critical value at which a quantum phase transition occurs, corresponding to the quasiparticle localization on clusters of local magnets (dimers, trimers, etc.) and to the onset of a Bose glass. Strong finite-size quantum fluctuations hinder further depletion of quasiparticles from such clusters, and thus lead to the appearance of pseudoplateaus in the magnetization curve of the system. On the other hand, site dilution hinders the field-induced Bose-Einstein condensation of triplet quasiparticles on the intact dimers, and it introduces instead a Bose glass of triplets. A thorough numerical investigation of the phase diagram for a planar system of coupled dimers shows that the two above-mentioned Bose glass phases are continuously connected, and they overlap in a finite region of parameter space, thus featuring a two-species Bose glass. The quantum phase transition from Bose glass to magnetically ordered phases in two dimensions is marked by novel universal exponents ($z\ensuremath{\approx}2$, $\ensuremath{\beta}\ensuremath{\approx}0.9$, and $\ensuremath{\nu}\ensuremath{\approx}1$). Hence we conclude that doped quantum antiferromagnets in a field represent an ideal setting for the study of fundamental dirty-boson physics.
Recent studies of delocalization-localization transitions in disordered quantum chains have highlighted the role of rare, chain-breaking events that favor localization, in particular for high-energy eigenstates related to many-body localization. In this context, we revisit the random-field XXZ spin-1/2 chain at zero temperature with ferromagnetic interactions, equivalent to interacting fermions or hard-core bosons in a random potential with attractive interactions. We argue that localization in this model can be characterized by chain-breaking events, which are probed by the extreme values of simple local observables, such as the on-site density or the local magnetization, that are readily accessible in both experiments and numerical simulations. Adopting a bosonic language, we study the disorder-induced Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition from superfluid (SF) to Bose glass (BG), and focus on the strong disorder regime where localization is driven by weak links. Based on high-precision density matrix renormalization group simulations, we numerically show that extreme local densities accurately capture the BKT transition, even for relatively short chains ranging from a few dozen to a hundred sites. We also discuss the SF-BG transition in the weak disorder regime, where finite-size effects pose greater challenges. Overall, our work seeks to establish a solid foundation for using extreme statistics of local observables, such as density, to probe delocalization-localization transitions in disordered quantum chains, both in the ground state and at high energy.