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Register a new user(1+1)-d U(1) Quantum link models from effective Hamiltonians of dipolar molecules
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We study the promising idea of using dipolar molecular systems as analog quantum simulators for quantum link models, which are discre
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We examine topological terms of $(2+1)$d sigma models and their consequences in the light of classifications of invertible quantum field theories utilizing bordism groups. In particular, we study the possible topological terms for the $U(N)/U(1)^N$ flag-manifold sigma model in detail. We argue that the Hopf-like term is absent, contrary to the expectation from a nontrivial homotopy group $pi_3(U(N)/U(1)^N)=mathbb{Z}$, and thus skyrmions cannot become anyons with arbitrary statistics. Instead, we find that there exist ${N(N-1)over 2}-1$ types of Chern-Simons terms, some of which can turn skyrmions into fermions, and we write down explicit forms of effective Lagrangians.
We present a worm-type Monte Carlo study of several typical models in the three-dimensional (3D) U(1) universality class, which include the classical 3D XY model in the directed flow representation and its Villain version, as well as the 2D quantum Bose-Hubbard (BH) model with unitary filling in the imaginary-time world-line representation. From the topology of the configurations on a torus, we sample the superfluid stiffness $rho_s$ and the dimensionless wrapping probability $R$. From the finite-size scaling analyses of $rho_s$ and of $R$, we determine the critical points as $T_c ({rm XY}) =2.201, 844 ,1(5)$ and $T_c ({rm Villain})=0.333, 067, 04(7)$ and $(t/U)_c ({rm BH})=0.059 , 729 ,1(8)$, where $T$ is the temperature for the classical models, and $t$ and $U$ are respectively the hopping and on-site interaction strength for the BH model. The precision of our estimates improves significantly over that of the existing results. Moreover, it is observed that at criticality, the derivative of a wrapping probability with respect to $T$ suffers from negligible leading corrections and enables a precise determination of the correlation length critical exponent as $ u=0.671 , 83(18)$. In addition, the critical exponent $eta$ is estimated as $eta=0.038 , 53(48)$ by analyzing a susceptibility-like quantity. We believe that these numerical results would provide a solid reference in the study of classical and quantum phase transitions in the 3D U(1) universality, including the recent development of the conformal bootstrap method.
Spin squeezing -- a central resource for quantum metrology -- results from the non-linear, entangling evolution of an initially factorized spin state. Here we show that universal squeezing dynamics is generated by a very large class of $S=1/2$ spin Hamiltonians with axial symmetry, in relationship with the existence of a peculiar structure of the low-lying Hamiltonian eigenstates -- the so-called Andersons tower of states. Such states are fundamentally related to the appearance of spontaneous symmetry breaking in quantum systems, and they are parametrically close to the eigenstates of a planar rotor (Dicke states), in that they feature an anomalously large value of the total angular momentum. We show that, starting from a coherent spin state, a generic $U(1)$-symmetric Hamiltonian featuring the Andersons tower of states generates the same squeezing evolution at short times as the one governed by the paradigmatic one-axis-twisting (or planar rotor) model of squeezing dynamics. The full squeezing evolution is seemingly reproduced for interactions decaying with distance $r$ as $r^{-alpha}$ when $alpha < 5d/3$ in $d$ dimensions. Our results connect quantum simulation with quantum metrology by unveiling the squeezing power of a large variety of Hamiltonian dynamics that are currently implemented by different quantum simulation platforms.
In this work, we study the $ U(1)/Z_2 $ Dicke model at a finite $ N $ by using the $ 1/J $ expansion and exact diagonization. This model includes the four standard quantum optics model as its various special limits. The $ 1/J $ expansions is complementary to the strong coupling expansion used by the authors in arXiv:1512.08581 to study the same model in its dual $ Z_2/U(1) $ representation. We identify 3 regimes of the systems energy levels: the normal, $ U(1) $ and quantum tunneling (QT) regime. The systems energy levels are grouped into doublets which consist of scattering states and Schrodinger Cats with even ( e ) and odd ( o ) parities in the $ U(1) $ and quantum tunneling (QT) regime respectively. In the QT regime, by the WKB method, we find the emergencies of bound states one by one as the interaction strength increases, then investigate a new class of quantum tunneling processes through the instantons between the two bound states in the compact photon phase. It is the Berry phase interference effects in the instanton tunneling event which leads to Schrodinger Cats oscillating with even and odd parities in both ground and higher energy bound states. We map out the energy level evolution from the $ U(1) $ to the QT regime and also discuss some duality relations between the energy levels in the two regimes. We also compute the photon correlation functions, squeezing spectrum, number correlation functions in both regimes which can be measured by various experimental techniques. The combinations of the results achieved here by $ 1/J $ expansion and those in arXiv:1512.08581 by strong coupling method lead to rather complete understandings of the $ U(1)/Z_2 $ Dicke model at a finite $ N $ and any anisotropy parameter $ beta $.
We report the observation of a resonance in the microwave spectra of the real diagonal conductivities of a two-dimensional electron system within a range of ~ +- .0.015 $ from filling factor $ u=1/3$. The resonance is remarkably similar to resonances previously observed near integer $ u$, and is interpreted as the collective pinning mode of a disorder-pinned Wigner solid phase of $e/3$-charged carriers .
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