Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems

We consider a quantum many-body system on a lattice with a continuous symmetry which exhibits a spontaneous symmetry breaking in its infinite volume ground states, but in which the order operator does not commute with the Hamiltonian. A typical example is the Heisenberg antiferromagnet with a Neel order. In the corresponding finite system, the symmetry breaking is usually "obscured" by "quantum fluctuation" and one gets a symmetric ground state with a long range order. In such a situation, we prove that there exist ever increasing numbers of low-lying eigenstates whose excitation energies are bounded by a constant times 1/N, where N denotes the number of sites. By forming linear combinations of these low-lying states and the (finite-volume) ground state, and by taking infinite volume limits, we construct infinite volume ground states with explicit symmetry breaking. Our general theorems do not only shed light on the nature ofsymmetry breaking in quantum many-body systems, but provide indispensable information for numerical approaches to these systems. We also discuss applications of our general results to a variety of examples. The present paper is intended to be accessible to the readers without background in mathematical approaches to quantum many-body systems.Comment: LaTeX, 58 pages, no figures. Notes about Bose-Einstein condenstaion are added after the publicatio

Hyponatremia and hypercalcemia: a study of a large cohort of patients with lung cancer

Background: Hyponatremia and hypercalcemia are reported to be associated with poorer prognosis in lung cancer. Our study assessed the incidence of hyponatremia and hypercalcemia in a recent large cohort of patients diagnosed with lung cancer in an academic institution and correlated incidence with patient and tumour parameters. Methods: All patients presented at our regional lung cancer multidisciplinary team meeting between January 2011 and December 2016 were included. The incidence of hyponatremia (serum sodium ≤135 mEq/L) and hypercalcemia (serum calcium >2.62 mmol/L), including severity (mild, moderate or severe) was evaluated and stratified by tumour subtype and stage, and correlated with patient parameters. Results: A total of 624 patients (mean age, 67.4 years; 59.3% male) diagnosed with tissue-proven lung cancer were included. Hyponatremia and hypercalcemia were present in 31.6% (n=197) and 7.1% (n=44) at time of diagnosis. Hyponatremia occurred most commonly in patients with small cell lung carcinoma (SCLC) (n=42; 41.2%; P=0.001). Hypercalcemia occurred most commonly in patients with non-small cell lung carcinoma (NSCLC) squamous subtype (n=27; 12.2%; P=0.003). The incidence of hyponatremia and hypercalcemia were significantly higher in the advanced stages (P<0.041), except in SCLC where no difference in hypercalcemia incidence across the stages was observed (P=0.573). The Eastern Cooperative Oncology Group Performance Status (ECOG-PS) score was positively correlated with severity of hyponatremia at the early stage of NSCLC (Spearman correlation coefficient =0.325; P=0.003). Conclusions: Hyponatremia is a common association in lung cancer, especially in SCLC. Hypercalcemia is an uncommon but significant association in the NSCLC squamous subtype. Hyponatremia might contribute to poorer ECOG-PS scores at the early stage of NSCLC

Influence of Hybridization on the Properties of the Spinless Falicov-Kimball Model

Without a hybridization between the localized f- and the conduction (c-) electron states the spinless Falicov-Kimball model (FKM) is exactly solvable in the limit of high spatial dimension, as first shown by Brandt and Mielsch. Here I show that at least for sufficiently small c-f-interaction this exact inhomogeneous ground state is also obtained in Hartree-Fock approximation. With hybridization the model is no longer exactly solvable, but the approximation yields that the inhomogeneous charge-density wave (CDW) ground state remains stable also for finite hybridization V smaller than a critical hybridization V_c, above which no inhomogeneous CDW solution but only a homogeneous solution is obtained. The spinless FKM does not allow for a ''ferroelectric'' ground state with a spontaneous polarization, i.e. there is no nonvanishing $$-expectation value in the limit of vanishing hybridization.Comment: 7 pages, 6 figure

Hybrid Monte Carlo with Fat Link Fermion Actions

The use of APE smearing or other blocking techniques in lattice fermion actions can provide many advantages. There are many variants of these fat link actions in lattice QCD currently, such as FLIC fermions. The FLIC fermion formalism makes use of the APE blocking technique in combination with a projection of the blocked links back into the special unitary group. This reunitarisation is often performed using an iterative maximisation of a gauge invariant measure. This technique is not differentiable with respect to the gauge field and thus prevents the use of standard Hybrid Monte Carlo simulation algorithms. The use of an alternative projection technique circumvents this difficulty and allows the simulation of dynamical fat link fermions with standard HMC and its variants. The necessary equations of motion for FLIC fermions are derived, and some initial simulation results are presented. The technique is more general however, and is straightforwardly applicable to other smearing techniques or fat link actions

Quantum fluctuations in quantum lattice-systems with continuous symmetry

We discuss conditions for the absence of spontaneous breakdown of continuous symmetries in quantum lattice systems at $T=0$. Our analysis is based on Pitaevskii and Stringari's idea that the uncertainty relation can be employed to show quantum fluctuations. For the one-dimensional systems, it is shown that the ground state is invariant under the continuous transformation if a certain uniform susceptibility is finite. For the two- and three-dimensional systems, it is shown that truncated correlation functions cannot decay any more rapidly than $|r|^{-d+1}$ whenever the continuous symmetry is spontaneously broken. Both of these phenomena occur owing to quantum fluctuations. Our theorems cover a wide class of quantum lattice-systems having not-too-long-range interactions.Comment: 14 pages. To appear in J.Stat.Phy

The spectral gap for some spin chains with discrete symmetry breaking

We prove that for any finite set of generalized valence bond solid (GVBS) states of a quantum spin chain there exists a translation invariant finite-range Hamiltonian for which this set is the set of ground states. This result implies that there are GVBS models with arbitrary broken discrete symmetries that are described as combinations of lattice translations, lattice reflections, and local unitary or anti-unitary transformations. We also show that all GVBS models that satisfy some natural conditions have a spectral gap. The existence of a spectral gap is obtained by applying a simple and quite general strategy for proving lower bounds on the spectral gap of the generator of a classical or quantum spin dynamics. This general scheme is interesting in its own right and therefore, although the basic idea is not new, we present it in a system-independent setting. The results are illustrated with an number of examples.Comment: 48 pages, Plain TeX, BN26/Oct/9

Optical lattice quantum simulator for QED in strong external fields: spontaneous pair creation and the Sauter-Schwinger effect

Spontaneous creation of electron-positron pairs out of the vacuum due to a strong electric field is a spectacular manifestation of the relativistic energy-momentum relation for the Dirac fermions. This fundamental prediction of Quantum Electrodynamics (QED) has not yet been confirmed experimentally as the generation of a sufficiently strong electric field extending over a large enough space-time volume still presents a challenge. Surprisingly, distant areas of physics may help us to circumvent this difficulty. In condensed matter and solid state physics (areas commonly considered as low energy physics), one usually deals with quasi-particles instead of real electrons and positrons. Since their mass gap can often be freely tuned, it is much easier to create these light quasi-particles by an analogue of the Sauter-Schwinger effect. This motivates our proposal of a quantum simulator in which excitations of ultra-cold atoms moving in a bichromatic optical lattice represent particles and antiparticles (holes) satisfying a discretized version of the Dirac equation together with fermionic anti-commutation relations. Using the language of second quantization, we are able to construct an analogue of the spontaneous pair creation which can be realized in an (almost) table-top experiment.Comment: 21 pages, 10 figure

Epitaxial growth of visible to infra-red transparent conducting In2O3 nanodot dispersions and reversible charge storage as a Li-ion battery anode

peer-reviewedUnique bimodal distributions of single crystal epitaxially grown In2O3 nanodots on silicon are shown to have excellent IR transparency greater than 87% at IR wavelengths up to 4 mu m without sacrificing transparency in the visible region. These broadband antireflective nanodot dispersions are grown using a two-step metal deposition and oxidation by molecular beam epitaxy, and backscattered diffraction confirms a dominant (111) surface orientation. We detail the growth of a bimodal size distribution that facilitates good surface coverage (80%) while allowing a significant reduction in In2O3 refractive index. This unique dispersion offers excellent surface coverage and three-dimensional volumetric expansion compared to a thin film, and a step reduction in refractive index compared to bulk active materials or randomly porous composites, to more closely match the refractive index of an electrolyte, improving transparency. The (111) surface orientation of the nanodots, when fully ripened, allows minimum lattice mismatch strain between the In2O3 and the Si surface. This helps to circumvent potential interfacial weakening caused by volume contraction due to electrochemical reduction to lithium, or expansion during lithiation. Cycling under potentiodynamic conditions shows that the transparent anode of nanodots reversibly alloys lithium with good Coulombic efficiency, buffered by co-insertion into the silicon substrate. These properties could potentially lead to further development of similarly controlled dispersions of a range of other active materials to give transparent battery electrodes or materials capable of non-destructive in situ spectroscopic characterization during charging and discharging.ACCEPTEDpeer-reviewe

A Characterization of Topological Insulators: Chern Numbers for a Ground State Multiplet

We propose to use generic Chern numbers for a characterization of topological insulators. It is suitable for a numerical characterization of low dimensional quantum liquids where strong quantum fluctuations prevent from developing conventional orders. By twisting parameters of boundary conditions, the non-Abelian Chern number are defined for a few low lying states near the ground state in a finite system, which is a ground state multiplet with a possible (topological) degeneracy. We define the system as a topological insulator when energies of the multiplet are well separated from the above. Translational invariant twists up to a unitary equivalence are crutial to pick up only bulk properties without edge states. As a simple example, the setup is applied for a two-dimensional $XXZ$-spin system with an ising anisotropy where the ground state multiplet is composed of doubly almost degenerate states. It gives a vanishing Chern number due to a symmetry. Also Chern numbers for the generic fractional quantum Hall states are discussed shortly.Comment: 2 figure

Two-Level Atom in an Optical Parametric Oscillator: Spectra of Transmitted and Fluorescent Fields in the Weak Driving Field Limit

We consider the interaction of a two-level atom inside an optical parametric oscillator. In the weak driving field limit, we essentially have an atom-cavity system driven by the occasional pair of correlated photons, or weakly squeezed light. We find that we may have holes, or dips, in the spectrum of the fluorescent and transmitted light. This occurs even in the strong-coupling limit when we find holes in the vacuum-Rabi doublet. Also, spectra with a sub-natural linewidth may occur. These effects disappear for larger driving fields, unlike the spectral narrowing obtained in resonance fluorescence in a squeezed vacuum; here it is important that the squeezing parameter $N$ tends to zero so that the system interacts with only one correlated pair of photons at a time. We show that a previous explanation for spectral narrowing and spectral holes for incoherent scattering is not applicable in the present case, and propose a new explanation. We attribute these anomalous effects to quantum interference in the two-photon scattering of the system.Comment: 10 pages, 17 figures, submitted to Phys Rev