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Register a new userLattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks
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Gauge theories are of paramount importance in our understanding of fundamental constituents of matter and their interactions. However, the complete characterization of their phase diagrams and the full understanding of non-perturbative effects are still debated, especially at finite charge density, mostly due to the sign-problem affecting Monte Carlo numerical simulations. Here, we report the Tensor Network simulation of a three dimensional lattice gauge theory in the Hamiltonian formulation including dynamical matter: Using this sign-problem-free method, we simulate the ground states of a compact Quantum Electrodynamics at zero and finite charge densities, and address fundamental questions such as the characterization of collective phases of the model, the presence of a confining phase at large gauge coupling, and the study of charge-screening effects.
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We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in $1+1$ space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic $c$-function that is finite. Unlike what happens in Lorentz-invariant theories, this $c$-function exhibits a strong violation of monotonicity; it also encodes the creation of long-range entanglement from the Fermi surface. Motivated by previous works on lattice models, we next calculate numerically the Renyi entropies and find Friedel-type oscillations; these are understood in terms of a defect operator product expansion. Furthermore, we consider the mutual information as a measure of correlation functions between different regions. Using a long-distance expansion previously developed by Cardy, we argue that the mutual information detects Fermi surface correlations already at leading order in the expansion. We also analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge and/or mass. In particular, we show that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy. Finally, we discuss possible extensions to interacting theories, and argue for the relevance of some of these measures for probing non-Fermi liquids.
To use quantum systems for technological applications we first need to preserve their coherence for macroscopic timescales, even at finite temperature. Quantum error correction has made it possible to actively correct errors that affect a quantum memory. An attractive scenario is the construction of passive storage of quantum information with minimal active support. Indeed, passive protection is the basis of robust and scalable classical technology, physically realized in the form of the transistor and the ferromagnetic hard disk. The discovery of an analogous quantum system is a challenging open problem, plagued with a variety of no-go theorems. Several approaches have been devised to overcome these theorems by taking advantage of their loopholes. Here we review the state-of-the-art developments in this field in an informative and pedagogical way. We give the main principles of self-correcting quantum memories and we analyze several milestone examples from the literature of two-, three- and higher-dimensional quantum memories.
We study 2d U(1) gauge Higgs systems with a $theta$-term. For properly discretizing the topological charge as an integer we introduce a mixed group- and algebra-valued discretization (MGA scheme) for the gauge fields, such that the charge conjugation symmetry at $theta = pi$ is implemented exactly. The complex action problem from the $theta$-term is overcome by exactly mapping the partition sum to a worldline/worldsheet representation. Using Monte Carlo simulation of the worldline/worldsheet representation we study the system at $theta = pi$ and show that as a function of the mass parameter the system undergoes a phase transition. Determining the critical exponents from a finite size scaling analysis we show that the transition is in the 2d Ising universality class. We furthermore study the U(1) gauge Higgs systems at $theta = pi$ also with charge 2 matter fields, where an additional $Z_2$ symmetry is expected to alter the phase structure. Our results indicate that for charge 2 a true phase transition is absent and only a rapid crossover separates the large and small mass regions.
In arXiv:1909.01269 it was shown that the scaling dimension of the lightest charge $n$ operator in the $U(1)$ model at the Wilson-Fisher fixed point in $d=4-varepsilon$ can be computed semiclassically for arbitrary values of $lambda n$, where $lambda$ is the perturbatively small fixed point coupling. Here we generalize this result to the fixed point of the $U(1)$ model in $3-varepsilon$ dimensions. The result interpolates continuously between diagrammatic calculations and the universal conformal superfluid regime for CFTs at large charge. In particular it reproduces the expectedly universal $O(n^0)$ contribution to the scaling dimension of large charge operators in $3d$ CFTs.
We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with $N$-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. It is known that there is no phase transition in the N=1 model. For N=2, we found that the system has a second-order phase transition line $tilde{c}_1(c_2)$ in the $c_2$(gauge coupling)$-c_1$(Higgs coupling) plane, which separates the confinement phase and the Higgs phase. Numerical results suggest that the phase transition belongs to the universality class of the 3D XY model as the previous works by Babaev et al. and Smiseth et al. suggested. For N=3, we found that there exists a critical line similar to that in the N=2 model, but the critical line is separated into two parts; one for $c_2 < c_{2{rm tc}}=2.4pm 0.1$ with first-order transitions, and the other for $ c_{2{rm tc}} < c_2$ with second-order transitions, indicating the existence of a tricritical point. We verified that similar phase diagram appears for the N=4 and N=5 systems. We also studied the case of anistropic Higgs coupling in the N=3 model and found that there appear two second-order phase transitions or a single second-order transition and a crossover depending on the values of the anisotropic Higgs couplings. This result indicates that an enhancement of phase transition occurs when multiple phase transitions coincide at a certain point in the parameter space.
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