Bosonic Limit Research Articles

Necessity of orthogonal basis vectors for the two-anyon problem in a one-dimensional lattice* *Supported by National Science Foundation of China (Grant Nos. 12074340 and 12474492) and the Science Foundation of Zhejiang Sci-Tech University (Grants No. 20062098-Y, 19062463-Y and 22062344-Y).

Few-body physics for anyons has been intensively studied within the anyon-Hubbard model, including the quantum walk and Bloch oscillations of two-anyon states. Recently, theoretical and experimental simulations of two-anyon states in a one-dimensional lattice have been carried out by expanding the wavefunction in terms of non-orthogonal basis vectors, resulting in non-physical degrees of freedom. In the present work, we deduce finite difference equations for the two-anyon state in a one-dimensional lattice by solving the Schrödinger equation with orthogonal and complete basis vectors. Such an orthogonal scheme gives all the orthogonal physical eigenstates, while the conventional (non-orthogonal) method produces many non-physical redundant eigensolutions whose components violate the anyonic commutation relations. The dynamical property of the two-anyon states in a sufficiently large lattice is investigated and compared in both the orthogonal and conventional schemes. For initial states with two anyons at the same site or two (next-)neighboring sites, we observe the same dynamical behavior in both schemes, including the revival probability, probability density function and two-body correlation. For other initial states, the conventional scheme produces erroneous states that no longer obey the anyonic relations. The period of Bloch oscillations in the pseudo-fermionic limit has been found to be twice that in the bosonic limit, while these oscillations disappear at other statistical parameters. Our findings are vital for quantum simulations of few-body anyonic physics in lattice models.

Supersymmetrizing the Pasti-Sorokin-Tonin action

In this paper the harmonic superspace action of the tensor multiplet of N = (1, 0), d = 6 supersymmetry is constructed which in the bosonic limit reduces to the known Pasti-Sorokin-Tonin action for the self-dual tensor field. The action involves, besides the potential containing the dynamical fields, also an auxiliary tensor multiplet and a set of analytic superfields with gauge PST scalar among them. For each of gauge symmetries of the PST action, a superfield analog is found. The equations of motion are calculated and it is shown that no extra degrees of freedom appear.

Distinguishing electroweak EFTs with WLWL→n×h

The electroweak symmetry-breaking sector is one of the most promising and uncharted parts of the Standard Model (SM); but it seems likely that new electroweak physics may be out of reach of the present accelerator effort and the hope is to observe small deviations from the SM. Given that, effective field theory (EFT) becomes the logic method to use, and Standard Model effective field theory (SMEFT) has become the standard. However, the most general theory with the known particle content is Higgs effective field theory (HEFT), and whether SMEFT suffices should be investigated in future experimental efforts. Building on investigations by other groups that established geometric criteria to distinguish SMEFT from HEFT (useful for theorists examining specific beyond-SM completions), we seek more phenomenological understanding and present an analogous discussion aimed at a broader audience. We discuss various aspects of (multi)Higgs boson production from longitudinal electroweak gauge bosons ${W}_{L}{W}_{L}\ensuremath{\rightarrow}n\ifmmode\times\else\texttimes\fi{}h$ in the TeV region as the necessary information to characterize the flare function, $\mathcal{F}(h)$, that determines whether SMEFT or HEFT is needed. We also present tree-level amplitudes including contact and exchange channels, as well as a short discussion on accessing $\mathcal{F}$ from the statistical limit of many bosons. We also discuss the status of the coefficients of the series expansion of $\mathcal{F}(h)$, its validity, whether its complex-$h$ extension can be used to predict or not a tell-tale zero, and how they relate to the dimension-six and -eight SMEFT operators in the electroweak sector. We derive a set of new correlations among beyond the standard model corrections to the HEFT coefficients that help decide, from experimental data, whether we have a viable SMEFT. This analysis can be useful for machines beyond the LHC that could address the challenging final state with several Higgs bosons.

Competing insulating phases in a dimerized extended Bose-Hubbard model

We study the ground-state properties of the extended Bose-Hubbard model in a one-dimensional dimerized optical lattice. In the limit of strong on-site repulsion, i.e., hardcore bosons, and strong nearest-neighbor interaction, a stable density-wave (DW) phase is obtained at half-filling as a function of lattice dimerization. Interestingly, at quarter-filling we obtain the signatures of an insulating phase which has the character of both the bond order (BO) and the DW insulators, which we call a bond-order density-wave (BODW) phase. Moreover, we show that for a fixed hopping dimerization there occurs a BO-DW phase crossover as a function of the nearest-neighbor interaction and the BODW phase is more robust when the hopping dimerization is stronger. We further examine the stability of the BODW phase in the limit of finite on-site interactions.

Transition between vacuum and finite-density states in the infinite-dimensional Bose–Hubbard model with spatially inhomogeneous dissipation

Abstract We analyze the dynamics of the infinite-dimensional Bose–Hubbard model with spatially inhomogeneous dissipation in the hardcore boson limit by solving the Lindblad master equation with use of the Gutzwiller variational method. We consider dissipation processes that correspond to inelastic light scattering in the case of Bose gases in optical lattices. We assume that the dissipation is applied to half of the lattice sites in a spatially alternating manner. We focus on steady states at which the system arrives after long time evolution. We find that when the average particle density is varied, the steady state exhibits a transition between a state in which the sites without dissipation are vacuum and one containing a finite number of particles at those sites. We associate the transition with the notion that the sites with dissipation tend towards a local state at infinite temperature.

Dissipative dynamics in the free massive boson limit of the sine-Gordon model

We study the dissipative dynamics of one-dimensional fermions, described in terms of the sine-Gordon model in its free massive boson or semi-classical limit, while keeping track of forward scattering processes. The system is prepared in the gapped ground state, and then coupled to environment through local currents within the Lindblad formalism. The heating dynamics of the system is followed using bosonization. The single particle density matrix exhibits correlations between the left and right moving particles. While the density matrix of right movers and left movers is translationally invariant, the left-right sector is not, corresponding to a translational symmetry breaking charge density wave state. Asymptotically, the single particle density matrix decays exponentially with exponent proportional to -\gamma t|x|\Delta^2−γt|x|Δ2 where \gammaγ and \DeltaΔ are the dissipative coupling and the gap, respectively. The charge density wave order parameter decays exponentially in time with an interaction independent decay rate. The second R'enyi entropy grows linearly with time and is essentially insensitive to the presence of the gap.

Quantum dynamics and correlations of indistinguishable anyons in one-dimensional lattices

Anyons, namely particles obeying fractional quantum statistics that interpolate between bosons and fermions, possess a lot of new and exotic physical properties related to the particle exchange statistics. In this work, we explore the few-body quantum dynamics and quantum correlations of indistinguishable anyons with on-site interactions in one-dimensional lattices within the scheme of three-body continuous-time quantum walks. By employing a time-evolving block decimation (TEBD) algorithm, we numerically calculate the dynamical evolution process of the local density distribution of anyons among the whole lattice. Numerical simulations shown in the main text mainly focus on a three-body initial state as <inline-formula><tex-math id="M1">\begin{document}$ \left|\psi(t=0)\right>=\hat{a}_{-1}^{\dagger}\hat{a}_{0}^{\dagger}\hat{a}_{1}^{\dagger}\left|0\right>$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20220188_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20220188_M1.png"/></alternatives></inline-formula>, in which three particles are located on neighbouring sites at lattice centre. This choice of initial state features that the three particles influence one another most strongly, while we have also implemented numerical simulations on other choices of three-body initial states as are discussed in appendix. It is shown that the local density distribution of anyons is dramatically altered by fractional particle statistics with new dynamical structure showing up during the time evolution. For free anyons, an inner cone emerges as the statistical parameter increases, while the outer cone remains robust all along. When the on-site interaction joins in, the structure of the inner cone is further modified with new features. Specifically, for interaction of finite strength, an exotic dynamical asymmetry in real space, is clearly demonstrated during the time evolution of the local density distribution for particles within the fractional statistics regime. However, for boson limit and pseudofermion limit, the time evolution of the local density distribution keeps symmetric as the three-body initial state. And remarkably, the dynamical asymmetry is interaction-dependent manifested as the local density distribution of anyons favors opposite side of the lattice for repulsive and attractive interaction, respectively. Moreover, when the on-site interaction is further increased to hard-core limit, the dynamical asymmetry will then be largely suppressed. We also calculate the density-density correlations for anyons before they reach the lattice boundary to reveal the interesting effect of fractional statistics on quantum correlations. It is shown that the inner cone corresponds to co-walking of anyons, while the outer cone is related to individual walking and is immune to the variation of statistical parameter. Furthermore, the exotic real-space asymmetry originated from the interplay of fractional statistics and finite interaction is also shown up in the density-density correlations.

Quantum Dynamics and Correlations of Indistinguishable Anyons in One-Dimensional Lattices

Anyons, namely particles obeying fractional quantum statistics that interpolate between bosons and fermions, possess a lot of new and exotic physical properties related to the particle exchange statistics. In this work, we explore the few-body quantum dynamics and quantum correlations of indistinguishable anyons with on-site interactions in onedimensional lattices within the scheme of three-body continuous-time quantum walks. By employing a time-evolving block decimation (TEBD) algorithm, we numerically calculate the dynamical evolution process of the local density distribution of anyons among the whole lattice. Numerical simulations shown in the main text mainly focus on a threebody initial state as ψ|(t=0)＞=â<sup>†</sup><sub>-1</sub>â<sup>†</sup><sub>0</sub>â<sup>†</sup><sub>1</sub>|0＞, in which three particles are located on neighbouring sites at lattice centre. This choice of initial state features that the three particles influence one another most strongly, while we have also implemented numerical simulations on other choices of three-body initial states as are discussed in appendix. It is shown that the local density distribution of anyons is dramatically altered by fractional particle statistics with new dynamical structure showing up during the time evolution. For free anyons, an inner cone emerges as the statistical parameter increases, while the outer cone remains robust all along. When the on-site interaction joins in, the structure of the inner cone is further modified with new features. Specifically, for interaction of finite strength, an exotic dynamical asymmetry in real space, is clearly demonstrated during the time evolution of the local density distribution for particles within the fractional statistics regime. However, for boson limit and pseudofermion limit, the time evolution of the local density distribution keeps symmetric as the three-body initial state. And remarkably, the dynamical asymmetry is interactiondependent manifested as the local density distribution of anyons favors opposite side of the lattice for repulsive and attractive interaction, respectively. Moreover, when the on-site interaction is further increased to hard-core limit, the dynamical asymmetry will then be largely suppressed. We also calculate the density-density correlations for anyons before they reach the lattice boundary to reveal the interesting effect of fractional statistics on quantum correlations. It is shown that the inner cone corresponds to co-walking of anyons, while the outer cone is related to individual walking and is immune to the variation of statistical parameter. Furthermore, the exotic real-space asymmetry originated from the interplay of fractional statistics and finite interaction is also shown up in the density-density correlations.

Dark matter from a complex scalar singlet: the role of dark CP and other discrete symmetries

We study the case of a pseudo-scalar dark matter candidate which emerges from a complex scalar singlet, charged under a global U(1) symmetry, which is broken both explicitly and spontaneously. The pseudo-scalar is naturally stabilized by the presence of a remnant discrete symmetry: dark CP. We study and compare the phenomenology of several simplified models with only one explicit symmetry breaking term. We find that several regions of the parameter space are able to reproduce the observed dark matter abundance while respecting direct detection and invisible Higgs decay limits: in the resonances of the two scalars, featuring the known as forbidden or secluded dark matter, and through non-resonant Higgs-mediated annihilations. In some cases, combining different measurements would allow one to distinguish the breaking pattern of the symmetry. Moreover, this setup admits a light DM candidate at the sub-GeV scale. We also discuss the situation where more than one symmetry breaking term is present. In that case, the dark CP symmetry may be spontaneously broken, thus spoiling the stability of the dark matter candidate. Requiring that this does not happen imposes a constraint on the allowed parameter space. Finally, we consider an effective field theory approach valid in the pseudo-Nambu-Goldstone boson limit and when the U(1) breaking scale is much larger than the electroweak scale.

Quantum Heat Engines with Singular Interactions

By harnessing quantum phenomena, quantum devices have the potential to outperform their classical counterparts. Here, we examine using wave function symmetry as a resource to enhance the performance of a quantum Otto engine. Previous work has shown that a bosonic working medium can yield better performance than a fermionic medium. We expand upon this work by incorporating a singular interaction that allows the effective symmetry to be tuned between the bosonic and fermionic limits. In this framework, the particles can be treated as anyons subject to Haldane’s generalized exclusion statistics. Solving the dynamics analytically using the framework of “statistical anyons”, we explore the interplay between interparticle interactions and wave function symmetry on engine performance.

Nonequilibrium dynamics from BCS to the bosonic limit

We investigate the quench dynamics of strongly coupled superconductors within the time-dependent Gutzwiller approximation from the BCS to the BEC regime and evaluate the out-of-equilibrium transient spectral density and optical conductivity relevant for pump probe experiments. Fourier transformation of the order parameter dynamics reveals a frequency $\Omega_J$ which, as in the BCS case, is controlled by the spectral gap. However, we find a crossover from the BCS dynamics to a new strong coupling regime where a characteristic frequency $\Omega_U$, associated to double occupancy fluctuations controls the order parameter dynamics. The change of regime occurs close to a dynamical phase transition. Both, $\Omega_J$ and $\Omega_U$ give rise to a complex structure of self-driven slow Rabi oscillations which are visible in the non-equilibrium optical conductivity where also side bands appear due to the modulation of the double occupancy by superconducting amplitude oscillations. Analogous results apply to CDW and SDW systems.

Non linear Schrödinger limit of bosonic ground states, again

I review an information-theoretic variant of the quantum de Finetti theorem due to Brandao and Harrow and discuss its applications to the topic of bosonic mean-field limits. This leads to slightly improved methods for the derivation of the local non-linear Schrodinger energy functional from many-body quantum mechanics.

Partial breaking of arbitrary amount of d=3 supersymmetry

Among the solutions of string theory and supergravity which preserve some fraction of supersymmetry, the best known are those that leave one half of the supersymmetry unbroken, and there is a large number of field theory models with this pattern of supersymmetry breaking. However, a lot of brane configurations exist which preserve only $1/4$, $1/8$ or more exotic fractions of supersymmetry, and field theory side of these systems remains largely unexplored. To find whether the formalism of nonlinear realizations is useful in construction of models of this type, we consider the systems of some $N_0$ scalar and vector $N=1$, $d=3$ Goldstone supermultiplets. We find that it is possible to construct an $SO(N_0)$ invariant theory of $N_0$ scalar multiplets with $N_0$ broken supersymmetries. For $N_0=3$ or $N_0\geq 5$ its action is not of Nambu-Goto type and its structure remains universal for arbitrary $N_0$. The cases of $N_0=1,2$ correspond to the membranes in $D=4$ and $D=5$, respectively, while for $N_0=4$ some arbitrariness in the action remains, and with proper choice of parameters, it is possible to obtain the action of the membrane in $D=7$ in the bosonic limit. It is also shown that the $SO(N_0)$ invariant action of $N_0$ vector multiplets with $1/N_0$ pattern of supersymmetry breaking does not exist for arbitrary $N_0$.

Supersymmetric Calogero Models from Superfield Gauging

Using the superfield gauging procedure, we construct new ${\cal N}\,{=}\,2$ and ${\cal N}\,{=}\,4$ superfield systems that generalize Calogero models. In the bosonic limit, these systems yield rational Calogero models and hyperbolic Calogero-Sutherland models in the ${\cal N}\,{=}\,2$ case, and their ${\rm U}(2)$ spin generalization in the ${\cal N}\,{=}\,4$ case.

Parafermion theory from the q-deformed algebra with q a root of unity

In this paper, we find the [Formula: see text]-deformed algebra with the finite- and infinite-dimensional Fock space and both the fermionic limit and the bosonic limit. Using the cardinality of set theory, we propose the Hamiltonian interpolating bosonic case and fermionic case, which enables us to construct the proper partition function and internal energy. As examples, we discuss the specific heat of free [Formula: see text] parafermion gas model and [Formula: see text] parafermion star.

Quantum entanglement in one-dimensional anyons

Anyons in one spatial dimension can be defined by correctly identifying the configuration space of indistinguishable particles and imposing Robin boundary conditions. This allows an interpolation between the bosonic and fermionic limits. In this paper, we study the quantum entanglement between two one-dimensional anyons on a real line as a function of their statistics.

Q-Deformed oscillator algebra in fermionic and bosonic limits

In this paper, the structure function corresponding to the q-deformed harmonic oscillator algebra is considered, where we construct the Hamiltonian by using creation and annihilation operators. Finally, the problem is investigated by evaluating the partition function of the system in finite- and infinite-dimensional Fock space for both fermionic and bosonic limits. Other thermodynamic properties such as the internal energy and the specific heat of the system are also calculated.

Non-Markovian features in semiconductor quantum optics: quantifying the role of phonons in experiment and theory

AbstractWe discuss phonon-induced non-Markovian and Markovian features in QD-based quantum nanooptics. We cover lineshapes in linear absorption experiments, phonon-induced incoherence in the Heitler regime, and memory correlations in two-photon coherences. To qualitatively and quantitatively understand the underlying physics, we present several theoretical models that capture the non-Markovian properties of the electron–phonon interaction accurately in different regimes. Examples are the Heisenberg equation of motion approach, the polaron master equation, and Liouville propagator techniques in the independent boson limit and beyond via the path integral method. Phenomenological modeling overestimates typically the dephasing due to the finite memory kernel of phonons and we give instructive examples of phonon-mediated coherence such as phonon-dressed anticrossings in Mollow physics, robust quantum state preparation, cavity feeding, and the stabilization of the collapse and revival phenomenon in the strong coupling limit of cavity quantum electrodynamics.

Topological charge pumping in the interacting bosonic Rice-Mele model

We investigate topological charge pumping in a system of interacting bosons in the tight-binding limit, described by the Rice-Mele model. An appropriate topological invariant for the many-body case is the change of polarization per pump cycle, which we compute for various interaction strengths from infinite-size matrix-product-state simulations. We verify that the charge pumping remains quantized as long as the pump cycle avoids the superfluid phase. In the limit of hardcore bosons, the quantized pumped charge can be understood from single-particle properties such as the integrated Berry curvature constructed from Bloch states, while this picture breaks down at finite interaction strengths. These two properties -- robust quantized charge transport in an interacting system of bosons and the breakdown of a single-particle invariant -- could both be measured with ultracold quantum gases extending a previous experiment [Lohse et al., Nature Phys. 12, 350 (2016)]. Furthermore, we investigate the entanglement spectrum of the Rice-Mele model and argue that the quantized charge pumping is encoded in a winding of the spectral flow in the entanglement spectrum over a pump cycle.

Quantum XX model with competing short- and long-range interactions: Phases and phase transitions in and out of equilibrium

We consider the quantum XX-model in the presence of competing nearest-neighbour and global-range interactions, which is equivalent to a Bose-Hubbard model with cavity mediated global range interactions in the hard core boson limit. Using fermionic techniques the problem is solved exactly in one dimension in the thermodynamic limit. The ground state phase diagram consists of two ordered phases: ferromagnetic (F) and antiferromagnetic (AF), as well as an XY-phase having quasi-long-range order. We have also studied quantum relaxation after sudden quenches. Quenching from the AF phase to the XY region remanent AF order is observed below a dynamical transition line. In the opposite quench, from the XY region to the AF-phase beyond a static metastability line AF order arises on top of remanent XY quasi-long-range order, which corresponds to dynamically generated supersolid state in the equivalent Bose-Hubbard model with hard-core bosons.