Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations

Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the "negative sign problem'' when applied to fermions - causing an exponential increase of the computing time with the number of particles. A polynomial time solution to the sign problem is highly desired since it would provide an unbiased and numerically exact method to simulate correlated quantum systems. Here we show, that such a solution is almost certainly unattainable by proving that the sign problem is NP-hard, implying that a generic solution of the sign problem would also solve all problems in the complexity class NP (nondeterministic polynomial) in polynomial time.Comment: 4 page

Super-Rough Glassy Phase of the Random Field XY Model in Two Dimensions

We study both analytically, using the renormalization group (RG) to two loop order, and numerically, using an exact polynomial algorithm, the disorder-induced glass phase of the two-dimensional XY model with quenched random symmetry-breaking fields and without vortices. In the super-rough glassy phase, i.e. below the critical temperature $T_c$, the disorder and thermally averaged correlation function $B(r)$ of the phase field $\theta(x)$, $B(r) = \bar{}$ behaves, for $r \gg a$, as $B(r) \simeq A(\tau) \ln^2 (r/a)$ where $r = |r|$ and $a$ is a microscopic length scale. We derive the RG equations up to cubic order in $\tau = (T_c-T)/T_c$ and predict the universal amplitude ${A}(\tau) = 2\tau^2-2\tau^3 + {\cal O}(\tau^4)$. The universality of $A(\tau)$ results from nontrivial cancellations between nonuniversal constants of RG equations. Using an exact polynomial algorithm on an equivalent dimer version of the model we compute ${A}(\tau)$ numerically and obtain a remarkable agreement with our analytical prediction, up to $\tau \approx 0.5$.Comment: 5 pages, 3 figure

Height fluctuations of a contact line: a direct measurement of the renormalized disorder correlator

We have measured the center-of-mass fluctuations of the height of a contact line at depinning for two different systems: liquid hydrogen on a rough cesium substrate and isopropanol on a silicon wafer grafted with silanized patches. The contact line is subject to a confining quadratic well, provided by gravity. From the second cumulant of the height fluctuations, we measure the renormalized disorder correlator Delta(u), predicted by the Functional RG theory to attain a fixed point, as soon as the capillary length is large compared to the Larkin length set by the microscopic disorder. The experiments are consistent with the asymptotic form for Delta(u) predicted by Functional RG, including a linear cusp at u=0. The observed small deviations could be used as a probe of the underlying physical processes. The third moment, as well as avalanche-size distributions are measured and compared to predictions from Functional RG.Comment: 6 pages, 14 figure

Pluripotency without Max

Myc/Max complexes are thought to be essential for maintaining pluripotency and self-renewal of embryonic stem cells (ESCs). In this issue of Cell Stem Cell, Hishida et al. (2011) provide genetic evidence that this requirement can be bypassed in well-defined culture conditions

SO(3) "Nuclear Physics" with ultracold Gases

An ab initio calculation of nuclear physics from Quantum Chromodynamics (QCD), the fundamental SU(3) gauge theory of the strong interaction, remains an outstanding challenge. Here, we discuss the emergence of key elements of nuclear physics using an SO(3) lattice gauge theory as a toy model for QCD. We show that this model is accessible to state-of-the-art quantum simulation experiments with ultracold atoms in an optical lattice. First, we demonstrate that our model shares characteristic many-body features with QCD, such as the spontaneous breakdown of chiral symmetry, its restoration at finite baryon density, as well as the existence of few-body bound states. Then we show that in the one-dimensional case, the dynamics in the gauge invariant sector can be encoded as a spin S=3/2 Heisenberg model, i.e., as quantum magnetism, which has a natural realization with bosonic mixtures in optical lattices, and thus sheds light on the connection between non-Abelian gauge theories and quantum magnetism.Comment: 34 pages, 9 figure

Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories

Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at non-zero temperature or baryon density. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can address the corresponding chiral dynamics in real time.Comment: 12 pages, 5 figures. Main text plus one basic introduction to the topic and one supplementary material on implementation. Final versio

Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits

A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.Comment: Published versio

Random RNA under tension

The Laessig-Wiese (LW) field theory for the freezing transition of random RNA secondary structures is generalized to the situation of an external force. We find a second-order phase transition at a critical applied force f = f_c. For f f_c, the extension L as a function of pulling force f scales as (f-f_c)^(1/gamma-1). The exponent gamma is calculated in an epsilon-expansion: At 1-loop order gamma = epsilon/2 = 1/2, equivalent to the disorder-free case. 2-loop results yielding gamma = 0.6 are briefly mentioned. Using a locking argument, we speculate that this result extends to the strong-disorder phase.Comment: 6 pages, 10 figures. v2: corrected typos, discussion on locking argument improve

An Interactive Tool to Explore and Improve the Ply Number of Drawings

Given a straight-line drawing $\Gamma$ of a graph $G=(V,E)$, for every vertex $v$ the ply disk $D_v$ is defined as a disk centered at $v$ where the radius of the disk is half the length of the longest edge incident to $v$. The ply number of a given drawing is defined as the maximum number of overlapping disks at some point in $\mathbb{R}^2$. Here we present a tool to explore and evaluate the ply number for graphs with instant visual feedback for the user. We evaluate our methods in comparison to an existing ply computation by De Luca et al. [WALCOM'17]. We are able to reduce the computation time from seconds to milliseconds for given drawings and thereby contribute to further research on the ply topic by providing an efficient tool to examine graphs extensively by user interaction as well as some automatic features to reduce the ply number.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Super-rough phase of the random-phase sine-Gordon model: Two-loop results

We consider the two-dimensional random-phase sine-Gordon and study the vicinity of its glass transition temperature $T_c$, in an expansion in small $\tau=(T_c-T)/T_c$, where $T$ denotes the temperature. We derive renormalization group equations in cubic order in the anharmonicity, and show that they contain two universal invariants. Using them we obtain that the correlation function in the super-rough phase for temperature $T<T_c$ behaves at large distances as $\bar{} = \mathcal{A}\ln^2(|x|/a) + \mathcal{O}[\ln(|x|/a)]$, where the amplitude $\mathcal{A}$ is a universal function of temperature $\mathcal{A}=2\tau^2-2\tau^3+\mathcal{O}(\tau^4)$. This result differs at two-loop order, i.e., $\mathcal{O}(\tau^3)$, from the prediction based on results from the "nearly conformal" field theory of a related fermion model. We also obtain the correction-to-scaling exponent.Comment: 34 page