Fractionalized conductivity and emergent self-duality near topological phase transitions

The experimental discovery of the fractional Hall conductivity in two-dimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange statistics. These anyons are usually studied deep inside an insulating topological phase. It is natural to ask whether such fractionalization can be detected more broadly, say near a phase transition from a conventional to a topological phase. To answer this question, we study a strongly correlated quantum phase transition between a topological state, called a $${{\mathbb{Z}}}_{2}$$ Z 2 quantum spin liquid, and a conventional superfluid using large-scale quantum Monte Carlo simulations. Our results show that the universal conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. Moreover, a dynamically self-dual optical conductivity emerges at low temperatures above the transition point, indicating the presence of the elusive vison particles. Our study opens the door for the experimental detection of anyons in a broader regime, and has ramifications in the study of quantum materials, programmable quantum simulators, and ultra-cold atomic gases. In the latter case, we discuss the feasibility of measurements in optical lattices using current techniques.

Superfluid Transition and Specific Heat of the 2D x-y Model: Monte Carlo Simulation

We present results of large-scale Monte Carlo simulations of the 2D classical x-y model on the square lattice. We obtain high accuracy results for the superfluid fraction and for the specific heat as a function of temperature, for systems of size L×L with L up to 212. Our estimate for the superfluid transition temperature is consistent with those furnished in all previous studies. The specific heat displays a well-defined peak, whose shape and position are independent of the size of the lattice for L>28, within the statistical uncertainties of our calculations. The implications of these results on the interpretation of experiments on adsorbed thin films of 4He are discussed.

Fragility of surface states in topological superfluid 3He

Superfluid 3He, with unconventional spin-triplet p-wave pairing, provides a model system for topological superconductors, which have attracted significant interest through potential applications in topologically protected quantum computing. In topological insulators and quantum Hall systems, the surface/edge states, arising from bulk-surface correspondence and the momentum space topology of the band structure, are robust. Here we demonstrate that in topological superfluids and superconductors the surface Andreev bound states, which depend on the momentum space topology of the emergent order parameter, are fragile with respect to the details of surface scattering. We confine superfluid 3He within a cavity of height D comparable to the Cooper pair diameter ξ0. We precisely determine the superfluid transition temperature Tc and the suppression of the superfluid energy gap, for different scattering conditions tuned in situ, and compare to the predictions of quasiclassical theory. We discover that surface magnetic scattering leads to unexpectedly large suppression of Tc, corresponding to an increased density of low energy bound states.

Tan’s two-body contact across the superfluid transition of a planar Bose gas

Tan’s contact is a quantity that unifies many different properties of a low-temperature gas with short-range interactions, from its momentum distribution to its spatial two-body correlation function. Here, we use a Ramsey interferometric method to realize experimentally the thermodynamic definition of the two-body contact, i.e., the change of the internal energy in a small modification of the scattering length. Our measurements are performed on a uniform two-dimensional Bose gas of 87Rb atoms across the Berezinskii–Kosterlitz–Thouless superfluid transition. They connect well to the theoretical predictions in the limiting cases of a strongly degenerate fluid and of a normal gas. They also provide the variation of this key quantity in the critical region, where further theoretical efforts are needed to account for our findings.

Nanospace-confined Helium Shows Four-dimensional Quantum Phase Transition (QPT)

Helium confined in a nanoporous material shows a four dimensional superfluid transition. This is a unique example of four dimensional critical phenomenon caused by strong quantum fluctuation.

Critical exponents of the O(N)-symmetric $$\phi ^4$$ model from the $$\varepsilon ^7$$ hypergeometric-Meijer resummation

We extract the $$\varepsilon $$ ε -expansion from the recently obtained seven-loop g-expansion for the renormalization group functions of the O(N)-symmetric model. The different series obtained for the critical exponents $$\nu ,\ \omega $$ ν , ω and $$\eta $$ η have been resummed using our recently introduced hypergeometric-Meijer resummation algorithm. In three dimensions, very precise results have been obtained for all the critical exponents for $$N=0,1,2,3$$ N = 0 , 1 , 2 , 3 and 4. To shed light on the obvious improvement of the predictions at this order, we obtained the divergence of the specific heat critical exponent $$\alpha $$ α for the XY model. We found the result $$-0.0123(11)$$ - 0.0123 ( 11 ) which is compatible with the famous experimental result of $$-0.0127(3)$$ - 0.0127 ( 3 ) from the specific heat of zero gravity liquid helium superfluid transition while the six-loop Borel with conformal mapping resummation result in literature gives the value $$-0.007(3)$$ - 0.007 ( 3 ) . For the challenging case of resummation of the $$\varepsilon $$ ε -expansion series in two dimensions, we showed that our resummation results reflect a significant improvement to the previous six-loop resummation predictions.

Universal sound diffusion in a strongly interacting Fermi gas

Transport of strongly interacting fermions is crucial for the properties of modern materials, nuclear fission, the merging of neutron stars, and the expansion of the early Universe. Here, we observe a universal quantum limit of diffusivity in a homogeneous, strongly interacting atomic Fermi gas by studying sound propagation and its attenuation through the coupled transport of momentum and heat. In the normal state, the sound diffusivity D monotonically decreases upon lowering the temperature, in contrast to the diverging behavior of weakly interacting Fermi liquids. Below the superfluid transition temperature, D attains a universal value set by the ratio of Planck’s constant and the particle mass. Our findings inform theories of fermion transport, with relevance for hydrodynamic flow of electrons, neutrons, and quarks.