Group-equivariant autoencoder for identifying spontaneously broken symmetries.

We introduce the group-equivariant autoencoder (GE autoencoder), a deep neural network (DNN) method that locates phase boundaries by determining which symmetries of the Hamiltonian have spontaneously broken at each temperature. We use group theory to deduce which symmetries of the system remain intact in all phases, and then use this information to constrain the parameters of the GE autoencoder such that the encoder learns an order parameter invariant to these "never-broken" symmetries. This procedure produces a dramatic reduction in the number of free parameters such that the GE-autoencoder size is independent of the system size. We include symmetry regularization terms in the loss function of the GE autoencoder so that the learned order parameter is also equivariant to the remaining symmetries of the system. By examining the group representation by which the learned order parameter transforms, we are then able to extract information about the associated spontaneous symmetry breaking. We test the GE autoencoder on the 2D classical ferromagnetic and antiferromagnetic Ising models, finding that the GE autoencoder (1) accurately determines which symmetries have spontaneously broken at each temperature; (2) estimates the critical temperature in the thermodynamic limit with greater accuracy, robustness, and time efficiency than a symmetry-agnostic baseline autoencoder; and (3) detects the presence of an external symmetry-breaking magnetic field with greater sensitivity than the baseline method. Finally, we describe various key implementation details, including a quadratic-programming-based method for extracting the critical temperature estimate from trained autoencoders and calculations of the DNN initialization and learning rate settings required for fair model comparisons.

Stable recursive auxiliary field quantum Monte Carlo algorithm in the canonical ensemble: Applications to thermometry and the Hubbard model.

Many experimentally accessible, finite-sized interacting quantum systems are most appropriately described by the canonical ensemble of statistical mechanics. Conventional numerical simulation methods either approximate them as being coupled to a particle bath or use projective algorithms which may suffer from nonoptimal scaling with system size or large algorithmic prefactors. In this paper, we introduce a highly stable, recursive auxiliary field quantum Monte Carlo approach that can directly simulate systems in the canonical ensemble. We apply the method to the fermion Hubbard model in one and two spatial dimensions in a regime known to exhibit a significant "sign" problem and find improved performance over existing approaches including rapid convergence to ground-state expectation values. The effects of excitations above the ground state are quantified using an estimator-agnostic approach including studying the temperature dependence of the purity and overlap fidelity of the canonical and grand canonical density matrices. As an important application, we show that thermometry approaches often exploited in ultracold atoms that employ an analysis of the velocity distribution in the grand canonical ensemble may be subject to errors leading to an underestimation of extracted temperatures with respect to the Fermi temperature.

Robust charge-density-wave correlations in the electron-doped single-band Hubbard model.

There is growing evidence that the hole-doped single-band Hubbard and t - J models do not have a superconducting ground state reflective of the high-temperature cuprate superconductors but instead have striped spin- and charge-ordered ground states. Nevertheless, it is proposed that these models may still provide an effective low-energy model for electron-doped materials. Here we study the finite temperature spin and charge correlations in the electron-doped Hubbard model using quantum Monte Carlo dynamical cluster approximation calculations and contrast their behavior with those found on the hole-doped side of the phase diagram. We find evidence for a charge modulation with both checkerboard and unidirectional components decoupled from any spin-density modulations. These correlations are inconsistent with a weak-coupling description based on Fermi surface nesting, and their doping dependence agrees qualitatively with resonant inelastic x-ray scattering measurements. Our results provide evidence that the single-band Hubbard model describes the electron-doped cuprates.

Parameter-free differential evolution algorithm for the analytic continuation of imaginary time correlation functions.

We report on differential evolution for analytic continuation: a parameter-free evolutionary algorithm to generate the dynamic structure factor from imaginary time correlation functions. Our approach to this long-standing problem in quantum many-body physics achieves enhanced spectral fidelity while using fewer compute (CPU) hours. The need for fine-tuning of algorithmic control parameters is eliminated by embedding them within the genome to be optimized for this evolutionary computation-based algorithm. Benchmarks are presented for models where the dynamic structure factor is known exactly and experimentally relevant results are included for quantum Monte Carlo simulations of bulk ^{4}He below the superfluid transition temperature.

Experimental realization of one dimensional helium.

As the spatial dimension is lowered, locally stabilizing interactions are reduced, leading to the emergence of strongly fluctuating phases of matter without classical analogues. Here we report on the experimental observation of a one dimensional quantum liquid of 4He using nanoengineering by confining it within a porous material preplated with a noble gas to enhance dimensional reduction. The resulting excitations of the confined 4He are qualitatively different than bulk superfluid helium, and can be analyzed in terms of a mobile impurity allowing for the characterization of the emergent quantum liquid beyond the Luttinger liquid paradigm. The low dimensional helium system offers the possibility of tuning via pressure-from weakly interacting, all the way to the super Tonks-Girardeau gas of strongly interacting hard-core particles.

Quantitation of Tissue Resection Using a Brain Tumor Model and 7-T Magnetic Resonance Imaging Technology.

BACKGROUND: Animal brain tumor models can be useful educational tools for the training of neurosurgical residents in risk-free environments. Magnetic resonance imaging (MRI) technologies have not used these models to quantitate tumor, normal gray and white matter, and total tissue removal during complex neurosurgical procedures. This pilot study was carried out as a proof of concept to show the feasibility of using brain tumor models combined with 7-T MRI technology to quantitatively assess tissue removal during subpial tumor resection. METHODS: Seven ex vivo calf brain hemispheres were used to develop the 7-T MRI segmentation methodology. Three brains were used to quantitate brain tissue removal using 7-T MRI segmentation methodology. Alginate artificial brain tumor was created in 4 calf brains to assess the ability of 7-T MRI segmentation methodology to quantitate tumor and gray and white matter along with total tissue volumes removal during a subpial tumor resection procedure. RESULTS: Quantitative studies showed a correlation between removed brain tissue weights and volumes determined from segmented 7-T MRIs. Analysis of baseline and postresection alginate brain tumor segmented 7-T MRIs allowed quantification of tumor and gray and white matter along with total tissue volumes removed and detection of alterations in surrounding gray and white matter. CONCLUSIONS: This pilot study showed that the use of animal tumor models in combination with 7-T MRI technology provides an opportunity to increase the granularity of data obtained from operative procedures and to improve the assessment and training of learners.

Rényi Generalization of the Accessible Entanglement Entropy.

Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect, Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)PRLTAO0031-900710.1103/PhysRevLett.91.097902] introduced an operational measure of the von Neumann entanglement entropy. Motivated by advances in measuring Rényi entropies in quantum many-body systems subject to conservation laws, we derive a generalization of the operationally accessible entanglement that is both computationally and experimentally measurable. Using the Widom theorem, we investigate its scaling with the size of a spatial subregion for free fermions and find a logarithmically violated area law scaling, similar to the spatial entanglement entropy, with at most a double-log leading-order correction. A modification of the correlation matrix method confirms our findings in systems of up to 10^{5} particles.

Theory of Liquid Film Growth and Wetting Instabilities on Graphene.

We investigate wetting phenomena near graphene within the Dzyaloshinskii-Lifshitz-Pitaevskii theory for light gases of hydrogen, helium, and nitrogen in three different geometries where graphene is either affixed to an insulating substrate, submerged or suspended. We find that the presence of graphene has a significant effect in all configurations. When placed on a substrate, the polarizability of graphene can increase the strength of the total van der Waals force by a factor of 2 near the surface, enhancing the propensity towards wetting. In a suspended geometry unique to two-dimensional materials, where graphene is able to wet on only one side, liquid film growth becomes arrested at a critical thickness, which may trigger surface instabilities and pattern formation analogous to spinodal dewetting. The existence of a mesoscopic critical film with a tunable thickness provides a platform for the study of a continuous wetting transition, as well as the engineering of custom liquid coatings. These phenomena are robust to some mechanical deformations and are also universally present in doped graphene and other two-dimensional materials, such as monolayer dichalcogenides.

Critical flow and dissipation in a quasi-one-dimensional superfluid.

In one of the most celebrated examples of the theory of universal critical phenomena, the phase transition to the superfluid state of (4)He belongs to the same three-dimensional (3D) O(2) universality class as the onset of ferromagnetism in a lattice of classical spins with XY symmetry. Below the transition, the superfluid density ρs and superfluid velocity v s increase as a power law of temperature described by a universal critical exponent that is constrained to be identical by scale invariance. As the dimensionality is reduced toward 1D, it is expected that enhanced thermal and quantum fluctuations preclude long-range order, thereby inhibiting superfluidity. We have measured the flow rate of liquid helium and deduced its superfluid velocity in a capillary flow experiment occurring in single 30-nm-long nanopores with radii ranging down from 20 to 3 nm. As the pore size is reduced toward the 1D limit, we observe the following: (i) a suppression of the pressure dependence of the superfluid velocity; (ii) a temperature dependence of v s that surprisingly can be well-fitted by a power law with a single exponent over a broad range of temperatures; and (iii) decreasing critical velocities as a function of decreasing radius for channel sizes below R ≃ 20 nm, in stark contrast with what is observed in micrometer-sized channels. We interpret these deviations from bulk behavior as signaling the crossover to a quasi-1D state, whereby the size of a critical topological defect is cut off by the channel radius.

4He Luttinger liquid in nanopores.

We study the low-temperature properties of a 4He fluid confined in nanopores, using large-scale quantum Monte Carlo simulations with realistic He-He and He-pore interactions. In the narrow-pore limit, the system can be described by the quantum hydrodynamic theory known as Luttinger liquid theory with a large Luttinger parameter, corresponding to the dominance of solid tendencies and strong susceptibility to pinning by a periodic or random potential from the pore walls. On the other hand, for wider pores, the central region appears to behave like a Luttinger liquid with a smaller Luttinger parameter, and may be protected from pinning by the wall potential, offering the possibility of experimental detection of a Luttinger liquid.

Dynamical conductivity at the dirty superconductor-metal quantum phase transition.

We study the transport properties of ultrathin disordered nanowires in the neighborhood of the superconductor-metal quantum phase transition. To this end we combine numerical calculations with analytical strong-disorder renormalization group results. The quantum critical conductivity at zero temperature diverges logarithmically as a function of frequency. In the metallic phase, it obeys activated scaling associated with an infinite-randomness quantum critical point. We extend the scaling theory to higher dimensions and discuss implications for experiments.

Infinite randomness fixed point of the superconductor-metal quantum phase transition.

We examine the influence of quenched disorder on the superconductor-metal transition, as described by a theory of overdamped Cooper pairs which repel each other. The self-consistent pairing eigenmodes of a quasi-one-dimensional wire are determined numerically. Our results support the recent proposal by Hoyos et al. [Phys. Rev. Lett. 99, 230601 (2007)10.1103/PhysRevLett.99.230601] that the transition is characterized by the same strong-disorder fixed point describing the onset of ferromagnetism in the random quantum Ising chain in a transverse field.