We study hard-core lattice bosons in a magnetic field near half filling. The bare vortex hopping rate is extracted from exact diagonalizations of square clusters. We deduce a quantum melting of the vortex lattice above vortex density of $6.5\times {10}^{-3}$ per lattice site. The Hall conductivity reverses sign abruptly as the density crosses half filling, where its characteristic temperature scale vanishes. We prove that at precisely half filling, each vortex carries a spin-$1/2$ quantum number (“$v$ spin”). Experimental implications of these results are discussed.

We explain how to combine holonomic quantum computation (HQC) with fault-tolerant quantum error correction. This establishes the scalability of HQC, putting it on equal footing with other models of computation, while retaining the inherent robustness the method derives from its geometric nature.

The ability to store quantum information without recourse to constant feedback processes would yield a significant advantage for future implementations of quantum information processing. In this Letter, limitations of the prototypical model, the Toric code in two dimensions, are elucidated along with a sufficient condition for overcoming these limitations. Specifically, the interplay between Hamiltonian perturbations and dynamically occurring noise is considered as a system in its ground state is brought into contact with a thermal reservoir. This proves that when utilizing the Toric code on $N^2$ qubits in a 2D lattice as a quantum memory, the information cannot be stored for a time $O(N)$. In contrast, the 2D Ising model protects classical information against the described noise model for exponentially long times. The results also have implications for the robustness of braiding operations in topological quantum computation.

We study the disorder-induced localization transition in a three-dimensional network model that belongs to symmetry class C. The model represents quasiparticle dynamics in a gapless spin-singlet superconductor without time-reversal invariance. It is a special feature of network models with this symmetry that the conductance and density of states can be expressed as averages in a classical system of dense, interacting random walks. Using this mapping, we present a more precise numerical study of critical behavior at an Anderson transition than has been possible previously in any context.

The major challenges to fabricate quantum processors and future nano-solid-state devices are material modification techniques with nanometer resolution and suppression of statistical fluctuations of dopants or qubit carriers. Based on a segmented ion trap with mK laser-cooled ions we have realized a deterministic single-ion source which could operate with a huge range of sympathetically cooled ion species, isotopes or ionic molecules. We have deterministically extracted a predetermined number of ions on demand and have measured a longitudinal velocity uncertainty of $6.3\mathrm{m}/\mathrm{s}$ and a spatial beam divergence of $600\mu \mathrm{rad}$. We show in numerical simulations that if the ions are cooled to the motional ground state (Heisenberg limit) nanometer spatial resolution can be achieved.

We study geometrical properties of interfaces in the random-temperature $q$-states Potts model as an example of a conformal field theory weakly perturbed by quenched disorder. Using conformal perturbation theory in $q-2$ we compute the fractal dimension of Fortuin-Kasteleyn (FK) domain walls. We also compute it numerically both via the Wolff cluster algorithm for $q=3$ and via transfer-matrix evaluations. We also obtain numerical results for the fractal dimension of spin clusters interfaces for $q=3$. These are found numerically consistent with the duality ${\kappa }^{\mathrm{spin}}{\kappa }^{\mathrm{FK}}=16$ as expressed in putative SLE parameters.

We present a method for determining the free energy of coexisting states from irreversible work measurements. Our approach is based on a fluctuation relation that is valid for dissipative transformations in partially equilibrated systems. To illustrate the validity and usefulness of the approach, we use optical tweezers to determine the free energy branches of the native and unfolded states of a two-state molecule as a function of the pulling control parameter. We determine, within $0.6k_{B}T$ accuracy, the transition point where the free energies of the native and the unfolded states are equal.

We study both mean-field and full quantum dynamics of symmetry-breaking transitions (SBTs) in a coupled two-component Bose-Einstein condensate. By controlling $s$-wave scattering lengths and the coupling strength, it is possible to stimulate SBTs between normal and spontaneously polarized ground states. In static transitions, the probability maxima of full quantum ground states correspond to the mean-field ground states. In dynamical transitions, due to the vanishing of excitation gaps, the mean-field dynamics shows universal scalings obeying the Kibble-Zurek mechanism. Both mean-field and full quantum defect modes appear as damped oscillations, but they appear at different critical points and undergo different oscillation regimes. The anomalous breakdown of mean-field dynamics induced by SBTs depends on the approaching direction.

A force applied to a spin-flipped particle in a one-dimensional spinor gas may lead to Bloch oscillations of the particle’s position and velocity. The existence of Bloch oscillations crucially depends on the viscous friction force exerted by the rest of the gas on the spin excitation. We evaluate the friction in terms of the quantum fluid parameters. In particular, we show that the friction is absent for integrable cases, such as an $SU(2)$ symmetric gas of bosons or fermions. For small deviations from the exact integrability the friction is very weak, opening the possibility to observe Bloch oscillations.

Building on recent neutron and NMR experiments, we investigate the field-induced exotic criticality observed in the frustrated compound ${\mathrm{BaCuSi}}_2{\mathrm{O}}_6$ using a frustrated model with two types of bilayers. A semiclassical treatment of the effective hard-core boson model shows that perfect interlayer frustration leads to a 2D-like critical exponent $\varphi =1$ without logarithmic corrections and to a 3D low temperature phase with different but nonvanishing triplet populations in both types of bilayers. These further suggest a simple phenomenology in terms of a field-dependent transverse coupling in the context of which we reproduce the entire field-temperature phase diagram with quantum Monte Carlo simulations.

Atomic Force microscope (AFM) cantilevers commonly used for imaging soft biological samples in liquids experience a momentary excitation of the higher eigenmodes at each tap. This transient response is very sensitive to the local sample elasticity under gentle imaging conditions because the higher eigenmode time period is comparable to the tip-sample contact time. By mapping the momentary excitation response, we demonstrate a new scanning probe spectroscopy capable of resolving with high sensitivity the variations in the elasticity of soft biological materials in liquids.

We show that failure of local realism can be revealed to observers for whom only extremely-coarse-grained measurements are available. In our instances, Bell’s inequality is violated even up to the maximum limit while both the local measurements and the initial local states under scrutiny approach the classical limit. Furthermore, we can observe failure of local realism when an inequality enforced by nonlocal realistic theories is satisfied. This suggests that locality alone may be violated while realism cannot be excluded for specific observables and states. Small-scale experimental demonstration of our examples may be possible in the foreseeable future.

We present a Coulomb gas method to calculate analytically the probability of rare events where the maximum eigenvalue of a random matrix is much larger than its typical value. The large deviation function that characterizes this probability is computed explicitly for Wishart and Gaussian ensembles. The method is general and applies to other related problems, e.g., the joint large deviation function for large fluctuations of top eigenvalues. Our results are relevant to widely employed data compression techniques, namely, the principal components analysis. Analytical predictions are verified by extensive numerical simulations.

The Casimir force due to a massless scalar field satisfying Dirichlet boundary conditions may draw a piston into the neck or toward the bulb of a flasklike container. In the worldline formalism this is due to competing contributions to the interaction energy from two types of Brownian bridges. Geometrical subtractions define a finite interaction energy. The procedure does not require regularization and appears well suited for numerical studies. The worldline analysis is robust with respect to variations in the shape of both piston and flask.

The microscopic properties of few interacting cold fermionic atoms confined in a two-dimensional (2D) harmonic trap are studied by numerical diagonalization. For repulsive interactions, a strong shell structure dominates, with Hund’s rule acting at its extreme for the midshell configurations. In the attractive case, odd-even oscillations due to pairing occur simultaneously with deformations in the internal structure of the ground states, as seen from pair correlation functions.

We present results from molecular dynamics simulations of water confined by two parallel atomically detailed hydrophobic walls. Simulations are performed at $T=300\mathrm{K}$ and wall-wall separation $d=0.6–1.6\mathrm{nm}$. At $0.7\le d\le 0.9\mathrm{nm}$, a first order transition occurs between a bilayer liquid (BL) and a trilayer heterogeneous fluid (THF) as water density increases. The THF is characterized by a liquid (central) layer and two crystal-like layers next to the walls. The BL-THF transition involves freezing of the two surface layers in contact with the walls. At $d=0.6\mathrm{nm}$, the THF transforms into a bilayer ice (BI) upon decompression. Both the BL-THF and BI-THF transitions are induced by the surface regular atomic-scale structure.

The dynamics of hard-core interacting Brownian particles in an external potential field is studied in one dimension. Using the Jepsen line we find a very general and simple formula relating the motion of the tagged center particle, with the classical, time dependent single particle reflection $\mathcal{R}$ and transmission $\mathcal{T}$ coefficients. Our formula describes rich physical behaviors both in equilibrium and the approach to equilibrium of this many body problem.

We study the driven dynamics of quantum coarsening. We analyze models of $M$-component rotors coupled to two electronic reservoirs at different chemical potential that generate a current threading through the system. In the large $M$ limit, we derive the dynamical phase diagram as a function of temperature, strength of quantum fluctuations, voltage, and coupling to the leads. We show that the slow relaxation in the ordering phase is universal. On large time and length scales, the dynamics are analogous to stochastic classical ones, even for the quantum system driven out of equilibrium at zero temperature. We argue that our results apply to generic driven quantum coarsening.

We study the intrinsic computational power of correlations exploited in measurement-based quantum computation. By defining a general framework, the meaning of the computational power of correlations is made precise. This leads to a notion of resource states for measurement-based classical computation. Surprisingly, the Greenberger-Horne-Zeilinger and Clauser-Horne-Shimony-Holt problems emerge as optimal examples. Our work exposes an intriguing relationship between the violation of local realistic models and the computational power of entangled resource states.

We define the direct and reverse secret-key capacities of a memoryless quantum channel as the optimal rates that entanglement-based quantum-key-distribution protocols can reach by using a single forward classical communication (direct reconciliation) or a single feedback classical communication (reverse reconciliation). In particular, the reverse secret-key capacity can be positive for antidegradable channels, where no forward strategy is known to be secure. This property is explicitly shown in the continuous variable framework by considering arbitrary one-mode Gaussian channels.