Session J8: Quantum Magnetism, BEC, and Disorder

Finite-$T$ spectral function of the BEC quantum magnets

We discuss the momentum, frequency, and temperature dependence of the spectral function of interacting 3D bosonic excitations in the vicinity of the BEC quantum critical point. The relaxation rate is demonstrated to have a highly non-trivial $\omega$-dependence with several asymptotic regimes that are studied in some detail. The spectral function is shown to exhibit, in a wide range of temperatures, an asymmetric quasiparticle peak and a shoulder, originating from the behavior of the self-energy. These spectral features should be readily observable in neutron-scattering experiments in the BEC quantum magnets. We also argue that this behavior of the spectral function must persist throughout the strong-coupling limit.   

Theory of magnetic Bose glass in Br-doped dichloro-tetrakis-thiourea-nickel (DTN)

We will review here the microscopic model allowing to describe quantitatively the physics of Br-doped DTN. The magnetic Hamiltonian of Br-DTN describes S=1 spins coupled through bimodally distributed antiferromagnetic bonds, and with a correlated bimodal distribution of single-ion anisotropies. A spin-boson mapping leads to a description in terms of a Bose-Hubbard-like model with random hoppings and random on-site interactions for magnetic quasiparticles, whose density is controlled by the applied magnetic field. This model features an extended gapless and compressible Bose-glass phase in low fields, extending down to zero field, at which the compressibility vanishes, corresponding to a Mott-glass phase. We will present extensive quantum Monte Carlo results for the thermodynamic signatures of the Bose glass, and for the quantum critical signatures of the magnetic ordering transition occurring at stronger field, which corresponds to a remarkable realization of the Bose-glass/superfluid transition.   

Magnetization and Specific Heat Investigations of the Bose Glass: Br-doped NiCl$_{2}$-4SC(NH$_{2}$)$_{2}$

NiCl$_{2}$-4SC(NH$_{2})_{2}$ (DTN) is an insulating material, which shows field induced XY-AFM order between $H_{c1}$ = 2.1 T and $H_{c2}$ = 12.6 T. In boson language, the ground state of DTN can be described as a Mott insulator, and the ordered state as a Bose-Einstein condensation of magnons. Bond disorder is introduced by substituting Br atoms on Cl positions, which simultaneously changes the super exchange interaction along the $c$-direction on a local scale and leads to a Mott-glass ground state in zero field. Furthermore, the system develops a gapless Bose glass for magnetic fields 0 $< \quad H \quad < \quad H_{c1}$ and $H \quad > \quad H_{c2}$, followed by a Mott insulating state above the saturation field $H_{sat}$. Note, that the critical fields $H_{c1,2}$ and $H_{sat}$ are shifted compared to those of pure DTN. In this talk, we report on measurements of the magnetization and specific heat at very low temperatures between 50 mK and 3 K in high magnetic fields up to 14 T on an 8{\%} Br-doped single crystal DTN. We compare our data with the local gap model, which reduces the low-temperature and low-field behavior to those of an ensemble of individual three level systems with local magnetization $M_{S}$ = 0, $\pm $1 and a finite energy gap for $H$ = 0.   

Magnetic Bose glass in Br-doped NiCl$_{2}$-4SC(NH$_{2})_{2}$: Magneto-Electric Effect

NiCl$_{1.85}$Br$_{0.15}$-4SC(NH$_{2})_{2}$ is a candidate for Bose glass state of the magnetism at low temperatures, which is the bosonic analog of Anderson localization. Here we explore the glassy dynamics of the magnetization taking advantage of magneto-electric coupling in this material. We report measurements of the magneto-electric effect in NiCl$_{1.85}$Br$_{0.15}$-4SC(NH$_{2})_{2}$ using two different experimental setups: (i) magnetic field-induced polarization and (ii) electric-field-induced magnetization. Both measurements show that the proposed Bose glass state in a high magnetic field is sensitive to the applied frequencies of AC magnetic and electric fields, with a maximum response between 700Hz and 1000Hz. This frequency-dependent behavior could provide information about the characteristic response time and the size of magnetic clusters.   

Disorder in a two-dimensional quantum spin liquid

We discuss magnetic field induced phase transition to magnon Bose-Einstein condensate state in a disordered two-dimensional spin gap antiferromagnet. Disorder was introduced into piperazinium hexachlorodicuprate (PHCC) by chemically substituting up to 10\% of exchange interaction mediating Cl ions for Br. We present specific heat, magnetization, susceptibility, elastic and inelastic neutron scattering results in fields up to 14T. Data reveals that disorder enlarges significantly the spin gap and induces nonzero susceptibility in the gapped phase. Reduction of magnon bandwidth and lifetime are evident from inelastic neutron scattering measurements. Although the phase transition seems to survive, the condensate wavefunction aquires a history dependence. In contrary to theoretical expectations, the extracted critical exponents show no changes within experimental accuracy.   

Dynamics of the Random-Field Ising Model

Ising magnets with long, needle-like domains can be treated as single extended spins which interact via dipole--dipole forces. Typically such dipole interactions cancel out due to spatial symmetry, but the combination of randomly packed grains and the application of a magnetic field transverse to the easy axis of magnetization can break the symmetry. This results in a site-random-magnetic field that points along the easy axis and varies from grain to grain, described by the Random--Field Ising Model (RFIM). We report a series of magnetization measurements in longitudinal and transverse magnetic fields that demonstrate RFIM behavior in the room--temperature, rare--earth ferromagnet Nd$_2$Fe$_{14}$B, and analyze our data in terms of predicted scaling relations.   

Strong Disorder Renormalization Group for the Many Body Localization Transition

The strong disorder renormalization group, originally devised by Ma and Dasgupta to study the random Heisenberg antiferromagnet, has subsequently been used to investigate the low energy physics and quantum phase transitions of a variety of strongly disordered systems. However, recent work by Basko, Aleiner, and Altshuler has focused attention on the many body localization transition, a dynamical quantum phase transition that involves the localization of highly excited eigenstates of a many body system in Fock space. Numerical results from an exact diagonalization study by Pal and Huse suggest that the many body localization transition may exhibit so-called infinite-randomness, a property that implies that a strong disorder renormalization group may be well-suited to study this transition. With the many body localization transition in mind, we therefore outline a strong disorder renormalization procedure that targets the least-localized eigenstate of a model. We then apply this procedure to study disordered quantum Ising and XXZ models. The latter model is similar to the one investigated by Pal and Huse and is expected to contain a dynamical transition between localized and ergodic phases; our principal aim is to use the strong disorder RG to characterize this transition.   

Evolution of magnetic order and fluctuations in Ni-V close to the disordered ferromagnetic quantum critical point

Muon spin rotation and magnetization data of the d-metal alloy Ni$_{1-x}$V$_{x}$ are presented at several vanadium concentrations $x$ below and above the critical $x_c \approx11\%$ where the onset of long-range ferromagnetic (FM) order is suppressed. Bulk magnetization shows signatures of a disordered quantum phase transition (QPT), most clearly in the paramagnetic regime: Above $x_c$ the temperature dependence of the magnetic susceptibility is best described by simple non-universal power laws marking a quantum Griffiths phase. But the deviations from a clean FM in the ordered phase are more subtle to recognize in the bulk magnetization and are noticed only close to $x_c$. Muon data reveal a broad field distribution in the FM regime at even small $x$ $(x \geq 4\%)$. The evolution of the magnetic cluster distribution and dynamics from the pristine FM towards the paramagnetic regime will be presented. This adds new insight in this model system at a disordered QPT.   

Unconventional spin-Peierls state in the quantum magnet TiOBr

The discovery of spin-Peierls transitions in inorganic materials such as CuGeO$_{3}$ with T$_{sp}$ of 14K allowed for the growth of large single crystals. With the availability of large single crystals the opportunity arises to introduce both magnetic and nonmagnetic impurities and study the resulting perturbations from the ground state. Recently a new class of unconventional spin-Peierls materials were discovered TiOBr and TiOCl. TiOBr and TiOCl have been shown to exhibit dimerized singlet ground states and undergo not one but two successive phase transitions. We have performed x-ray scattering measurements on single crystals of TiOBr. These measurements reveal both commensurate and incommensurate spin-Peierls phases; below T$_{c2}$ $\sim$48K incommensurate super-lattice reflections arise at Q=[H$\pm$$\delta$,K+1/2$\pm$$\epsilon$,L] which persists down to the lock in transition at T$_{c1}$$\sim$27K. We will report on the details of these successive transitions and the destruction of the long-range ordered spin-Peierls state with introduction of magnetic vacancies by doping with Sc.   

Ashkin-Teller criticality and pseudo-first-order behavior in a frustrated Ising model on the square lattice

We consider the square-lattice frustrated Ising model with first- and second-neighbor interactions, $J_1<0$ and $J_2>0$. Its thermal phase transition to ``stripe'' order when $g=J_2/|J_1|>1/2$ has remained controversial despite many past studies. Using Monte Carlo simulations to investigate the order-parameter distribution and its Binder cumulant, we demonstrate Ashkin-Teller criticality for $g \ge g^*$, i.e., the critical exponents vary continuously between those of the $4$-state Potts model at $g^*$ and the Ising model for $g \to \infty$. The Potts point, below which the transition is first-order, is $g^*= 0.67 \pm 0.01$, much lower than previously believed. The system exhibits {\it pseudo first-order} behavior for $g^* \le g \le g^{\prime}\ (g^{\prime}\approx 0.9)$, which was previously misinterpreted as actual first-order behavior.   

Quantum phase diagram of the spin ladder model with next-nearest neighbor interactions

By using the density matrix renormalization group technique, we investigate the quantum phase diagram of a two-leg spin-1/2 ladder with diagonal and in-chain next-nearest neighbor interactions for both anti-ferromagnetic and ferromagnetic frustrated cases. Through analyzing the correlation function and four-site entropy, the existence of the controversial columnar dimer phase is confirmed, and the phase transitions caused by the in-chain next-nearest neighbor interaction are presented for the anti-ferromagnetic frustrated case; meanwhile, for the ferromagnetic frustrated case, we find that the system possesses a tetramer phase, a ferromagnetic phase, and the states I and II, and the spin arrangements for I and II are determined.   

Majorana Spin Liquids on a two-leg ladder

We realize a gapless Majorana Orbital Liquid (MOL) using orbital degrees of freedom and also an SU(2)-invariant Majorana Spin Liquid (MSL) using both spin and orbital degrees of freedom in Kitaev-type models on a 2-leg ladder. The models are exactly solvable by Kitaev's parton approach, and we obtain long-wavelength descriptions for both Majorana liquids. The MOL has one gapless mode and power law correlations in energy at incommensuare wavevectors, while the SU(2) MSL has three gapless modes and power law correlations in spin, spin-nematic, and local energy observables. We study the stability of such states to perturbations away from the exactly solvable points. We find that both MOL and MSL can be stable against allowed short-range parton interactions. We also argue that both states persist upon allowing $Z_2$ gauge field fluctuations, in that the number of gapless modes is retained, although with an expanded set of contributions to observables compared to the free parton mean field.   

Static and dynamic properties of a strong-leg spin ladder

Static and dynamic properties of the strong-leg S = 1/2 Heisenberg spin ladder system (C$_7$H$_{10}$N)$_2$CuBr$_4$ are studied using inelastic neutron scattering and neutron diffraction experiments, as well as bulk magneto-thermodynamic measurements. The leg-odd excitation channel is dominated by long-lived single-magnon states in the entire Brillouin zone, which supports a symmetric-ladder model for this material [1]. In the leg-even channel, a considerable fraction of the spectral weight is contained in a novel long-lived two-magnon bound state. Contrary to reports by other authors, in applied magnetic fields we observe a Bose-Einstein condensation of magnons that manifests itself if 3D long-range antiferromagnetic ordering. The latter emerges beyond $H_c$=2.8 T and is due to weak inter-chain interactions. The field-temperature phase diagram showing the spin liquid, Tomonaga-Luttinger spin liquid and BEC phases is mapped out. The experimental results are in spectacular agreement with DMRG calculations. The latter provide additional insight on certain spin ladder properties specific to the strong-leg regime. \\[4pt] [1] D. Schmidiger, S. M\"uhlbauer, S. N. Gvasaliya, T. Yankova, and A. Zheludev Phys. Rev. B 84, 144421 (2011).   

Sign problem free quantum Monte Carlo simulations of spin density wave transitions in metals

We present a version of the spin-fermion model for spin density wave (SDW) transitions in metals, which can be simulated using the determinant quantum Monte Carlo method with no sign problem. The sign problem is eliminated by generalizing the model to include two orbitals which are coupled through the SDW field. The resulting model has a pseudo-time reversal symmetry that guarantees that the minus signs resulting from integrating out the fermions cancel, resulting in a real effective action for the SDW bosonic field. We present preliminary results for the SDW and pairing susceptibilities and the fermion Green's function near the quantum critical point.