Bosonic Degrees Of Freedom Research Articles

Exotic compact objects and light bosonic fields

In this article, we discuss the effect of light, nongauge, bosonic degrees of freedom on the exterior spacetime of an exotic compact object. We show that such fields generically introduce large deviations from black hole spacetimes of general relativity near and outside the surfaces of ultracompact exotic objects unless one assumes they totally decouple from the standard model or new heavy fields. Hence, using black hole spacetimes of general relativity to model ultracompact exotic objects and their perturbations relies implicitly on this assumption or on the absence of such fields. Published by the American Physical Society 2024

Fuzzy gauge theory for quantum computers

Continuous gauge theories, because of their bosonic degrees of freedom, have an infinite-dimensional local Hilbert space. Encoding these degrees of freedom on qubit-based hardware demands some sort of “qubitization” scheme, where one approximates the behavior of a theory while using only finitely many degrees of freedom. We propose a novel qubitization strategy for gauge theories, called “fuzzy gauge theory,” building on the success of the fuzzy σ-model in earlier work. We provide arguments that the fuzzy gauge theory lies in the same universality class as regular gauge theory, in which case its use would obviate the need of any further limit besides the usual spatial continuum limit. Furthermore, we demonstrate that these models are relatively resource-efficient for quantum simulations. Published by the American Physical Society 2024

Chiral limit of a fermion-scalar (1/2)+ system in covariant gauges

The homogeneous Bethe-Salpeter equation (BSE) of a (1/2)$^+$ bound system, that has both fermionic and bosonic degrees of freedom, that we call a {\em mock nucleon}, is studied in Minkowski space, in order to analyse the chiral limit in covariant gauges. After adopting an interaction kernel built with a one-particle exchange, the $\chi$-BSE is numerically solved by means of the Nakanishi integral representation and light-front projection. Noteworthy, the chiral limit induces a scale-invariance of the model and consequently generates a wealth of striking features: i) it reduces the number of non trivial Nakanishi weight functions to only one; ii) the form of the surviving weight function has a factorized dependence on the two relevant variables, compact and non-compact one; iii) the coupling constant becomes an explicit function of the real exponent governing the power-law fall-off of the non trivial Nakanishi weight function. The thorough investigation at large transverse-momentum of light-front Bethe-Salpeter amplitudes, obtained with massive constituents, provides a confirmation of the expected universal power-law fall-off, with exponents predicted by our non-perturbative framework. Finally, one can shed light on the exponents that govern the approach to the upper extremum of the longitudinal-momentum fraction distribution function of the {\em mock nucleon}, when the coupling constant varies.

Chebyshev pseudosite matrix product state approach for the spectral functions of electron-phonon coupling systems

The electron-phonon ($e$-ph) coupling system often has a large number of phonon degrees of freedom, whose spectral functions are numerically difficult to compute using matrix product state (MPS) formalisms. To solve this problem, we propose a new and practical method that combines the Chebyshev MPS and the pseudosite density matrix renormalization group (DMRG) algorithm. The Chebyshev vector is represented by a pseudosite MPS with global $U(1)$ fermion symmetry, which maps $2^{N_p}$ bosonic degrees of freedom onto $N_p$ pseudosites, each with two states. This approach can handle arbitrary $e$-ph coupling Hamiltonians where pseudosite DMRG performs efficiently. We use this method to study the spectral functions of the doped extended Hubbard-Holstein model in a regime of strong Coulomb repulsion, which has not been studied extensively before. Key features of the excitation spectra are captured at a modest computational cost. Our results show that weak extended $e$-ph couplings can increase the spectral weight of the holon-folding branch at low phonon frequencies, in agreement with angle-resolved photoemission observations on one-dimensional (1D) cuprates.

Structured ground states of randomly interacting bosons

Bosonic degrees of freedom and their emergence as part of complex quantum many-body dynamics, symmetries, collective behavior, clustering, and phase transitions play an important role in modern studies of quantum systems. In this paper, we present a systematic study of many-boson systems governed by random interactions. Our findings show that ground states of randomly interacting bosons are not random, being dominated by a few collective configurations containing condensates of clusters.

Quantum counterpart of energy equipartition theorem for fermionic systems

In this brief report, following the recent developments on formulating a quantum analogue of the classical energy equipartition theorem for open systems where the heat bath comprises of independent oscillators, i.e. bosonic degrees of freedom, we present an analogous result for fermionic systems. The most general case where the system is connected to multiple reservoirs is considered and the mean energy in the steady state is expressed as an integral over the reservoir frequencies. Physically this would correspond to summing over the contributions of the bath degrees of freedom to the mean energy of the system over a suitable distribution function ρ(ω) dependent on the system parameters. This result holds for nonequilibrium steady states, even in the nonlinear regime far from equilibrium. We also analyze the zero temperature behaviour and low temperature corrections to the mean energy of the system.

Towards top-down holographic composite Higgs: minimal coset from maximal supergravity

Within the context of top-down holography, we study a one-parameter family of regular background solutions of maximal gauged supergravity in seven dimensions, dimensionally reduced on a 2-torus. The dual, four-dimensional confining field theory realises the global (spontaneous as well as explicit) symmetry breaking pattern SO(5) → SO(4). We compute the complete mass spectrum for the fluctuations of the 128 bosonic degrees of freedom of the five-dimensional gravity theory, which correspond to scalar, pseudoscalar, vector, axial-vector, and tensor bound states of the dual field theory, and includes particles with exotic SO(4) quantum numbers. We confirm the existence of tachyonic instabilities near the boundaries of the parameter space.We discuss the interplay between explicit and spontaneous symmetry breaking. The SO(5)/SO(4) coset might provide a first step towards the realisation of a calculable framework and ultraviolet completion of minimal composite Higgs models, if the four pseudo-Nambu-Goldstone bosons are identified with the real components of the Higgs doublet in the standard model (SM), and a subgroup of SO(4) with the SU(2) × U(1) SM gauge group. We exhibit an example with an additional localised boundary term that mimics the effect of a weakly-coupled external sector.

Supersymmetric free fermions and bosons: Locality, symmetry, and topology

Supersymmetry, originally proposed in particle physics, refers to a dual relation that connects fermionic and bosonic degrees of freedom in a system. Recently, there has been considerable interest in applying the idea of supersymmetry to topological phases, motivated by the attempt to gain insights from the fermion side into the boson side and vice versa. We present a systematic study of this construction when applied to band topology in noninteracting systems. First, on top of the conventional ten-fold way, we find that topological insulators and superconductors are divided into three classes depending on whether the supercharge can be local and symmetric, must break a symmetry to preserve locality, or needs to break locality. Second, we resolve the apparent paradox between the nontriviality of free fermions and the triviality of free bosons by noting that the topological information is encoded in the identification map. We also discuss how to understand a recently revealed supersymmetric entanglement duality in this context. These findings are illustrated by prototypical examples. Our work sheds new light on band topology from the perspective of supersymmetry.

From the open generalized Heisenberg model to the Landau–Lifshitz equation

Magnetic systems can be described by the classical Landau–Lifshitz (LL) equation or the fully quantum open generalized Heisenberg model. Using the Lindblad master equation and the mean-field approximation, we demonstrate that the open generalized Heisenberg model is reduced to a generalized LL equation. The open dynamic is modeled using spin-boson interactions with a common bosonic reservoir at thermal equilibrium. By tracing out the bosonic degrees of freedom, we obtain two different decoherence mechanisms: on-site dissipation and an effective spin–spin interaction mediated by bosons. Using our approach, we perform hysteresis calculations, closely connected with the Stoner–Wohlfarth theory. We compare the exact numerical master equation and the mean-field model, revealing the role of correlations originated by non-local interactions. Our work opens new horizons for the study of the LL dynamics from an open quantum formalism.

Adinkra foundation of component decomposition and the scan for superconformal multiplets in 11D, mathcal{N} = 1 superspace

For the first time in the physics literature, the Lorentz representations of all 2,147,483,648 bosonic degrees of freedom and 2,147,483,648 fermionic degrees of freedom in an unconstrained eleven dimensional scalar superfield are presented. Comparisons of the conceptual bases for this advance in terms of component field, superfield, and adinkra arguments, respectively, are made. These highlight the computational efficiency of the adinkra-based approach over the others. It is noted at level sixteen in the 11D, mathcal{N} = 1 scalar superfield, the {65} representation of SO(1,10), the conformal graviton, is present. Thus, adinkra-based arguments suggest the surprising possibility that the 11D, mathcal{N} = 1 scalar superfield alone might describe a Poincaré supergravity prepotential or semi-prepotential in analogy to one of the off-shell versions of 4D, mathcal{N} = 1 superfield supergravity. We find the 11D, mathcal{N} = 1 scalar superfield contains 1,494 bosonic fields, 1,186 fermionic fields, and a maximum number of 29,334 links connecting them via orbits of the supercharges.

Entanglement-spectrum characterization of ground-state nonanalyticities in coupled excitation-phonon models

The polaron concept captures physical situations involving an itinerant quantum particle (excitation) that interacts strongly with bosonic degrees of freedom and becomes heavily boson-dressed. While the Gerlach-L\"{o}wen theorem rules out the occurrence of nonanalyticities of ground-state-related quantities for a broad class of polaron models, examples were found in recent years of sharp transitions pertaining to strongly momentum-dependent interactions of an excitation with dispersionless (zero-dimensional) phonons. On the example of a lattice model with Peierls-type excitation-phonon interaction, such level-crossing-type small-polaron transitions are analyzed here through the prism of the entanglement spectrum of the excitation-phonon system. By evaluating this spectrum in a numerically-exact fashion it is demonstrated that the behavior of the entanglement entropy in the vicinity of the critical excitation-phonon coupling strength chiefly originates from one specific entanglement-spectrum eigenvalue, namely the smallest one. While the discrete translational symmetry of the system implies that those eigenvalues can be labeled by the bare-excitation quasimomentum quantum numbers, here it is shown numerically that they are predominantly associated to the quasimomenta $0$ and $\pi$, including cases where a transition between the two takes place deeply in the strong-coupling regime.

Mølmer–Sørensen entangling gate for cavity QED systems

The Mølmer–Sørensen gate is a state-of-the-art entangling gate in ion trap quantum computing where the gate fidelity can exceed 99%. Here we propose an analogous implementation in the setting of cavity QED. The cavity photon mode acts as the bosonic degree of freedom in the gate in contrast to that played by the phonon mode in ion traps. This is made possible by utilising cavity assisted Raman transitions interconnecting the logical qubit states embedded in a four-level energy structure, making the ‘anti-Jaynes–Cummings’ term available under the rotating-wave approximation. We identify practical sources of infidelity and discuss their effects on the gate performance. Our proposal not only demonstrates an alternative entangling gate scheme but also sheds new light on the relationship between ion traps and cavity QED, in the sense that many techniques developed in the former are transferable to the latter through our framework.

Thermal Schrödinger Equation: Efficient Tool for Simulation of Many‐Body Quantum Dynamics at Finite Temperature

AbstractWe develop a wave‐function‐based method for the simulation of quantum dynamics of systems with many degrees of freedom at finite temperature. The method is inspired by the ideas of Thermo Field Dynamics (TFD). As TFD, our method is based on the doubling of the system's degrees of freedom and thermal Bogoliubov transformation. As distinct from TFD, our method implements the doubling of thermalized degrees of freedom only, and relies upon the explicitly constructed generalized thermal Bogoliubov transformation, which is not restricted to fermionic and bosonic degrees of freedom. This renders the present approach computationally efficient and applicable to a large variety of systems.

Nonequilibrium GW+EDMFT: Antiscreening and Inverted Populations from Nonlocal Correlations.

We study the dynamics of screening in photodoped Mott insulators with long-ranged interactions using a nonequilibrium implementation of the GW plus extended dynamical mean-field theory formalism. Our study demonstrates that the complex interplay of the injected carriers with bosonic degrees of freedom (charge fluctuations) can result in long-lived transient states with properties that are distinctly different from those of thermal equilibrium states. Systems with strong nonlocal interactions are found to exhibit a self-sustained population inversion of the doublons and holes. This population inversion leads to low-energy antiscreening which can be detected in time-resolved electron-energy-loss spectra.

Analog quantum simulation of(1+1)-dimensional lattice QED with trapped ions

The prospect of quantum simulating lattice gauge theories opens exciting possibilities for understanding fundamental forms of matter. Here, we show that trapped ions represent a promising platform in this context when simultaneously exploiting internal pseudo-spins and external phonon vibrations. We illustrate our ideas with two complementary proposals for simulating lattice-regularized quantum electrodynamics (QED) in (1+1) space-time dimensions. The first scheme replaces the gauge fields by local vibrations with a high occupation number. By numerical finite-size scaling, we demonstrate that this model recovers Wilson's lattice gauge theory in a controlled way. Its implementation can be scaled up to tens of ions in an array of micro-traps. The second scheme represents the gauge fields by spins 1/2, and thus simulates a quantum link model. As we show, this allows the fermionic matter to be replaced by bosonic degrees of freedom, permitting small-scale implementations in a linear Paul trap. Both schemes work on energy scales significantly larger than typical decoherence rates in experiments, thus enabling the investigation of phenomena such as string breaking, Coleman's quantum phase transition, and false-vacuum decay. The underlying ideas of the proposed analog simulation schemes may also be adapted to other platforms, such as superconducting qubits.

U(1) chiral symmetry in a one-dimensional interacting electron system with spin

We study a spin dependent Tomonaga-Luttinger model in one dimension, which describes electron transport through a single barrier. Using the Fermi-Bose equivalence in one dimension, we map the model onto a massless Thirring model with a boundary interaction. A field theoretical perturbation theory for the model has been developed and the chiral symmetry is found to play an important role. The classical bulk action possesses a global $U_A(1)^4$ chiral symmetry, since the fermion fields are massless. This global chiral symmetry is broken by the boundary interaction and the bosonic degrees of freedom, corresponding to the chiral phase transformation, become dynamical. They acquire an additional kinetic action from the fermion path integral measure and govern the critical behaviors of physical operators. On the critical line where the boundary interaction becomes marginal, they decouple from the fermi fields. Consequently the action reduces to the free field action, which contains only a fermion bilinear boundary mass term as an interaction term. By a renormalization group analysis, we obtain a new critical line, which differs from the previously known critical lines in the literature. The result of this work implies that the phase diagram of the one dimensional electron system may have a richer structure than previously known.

Duality group actions on fermions

In this short paper we look at the action of T-duality and string duality groups on fermions, in maximally-supersymmetric theories and related theories. Briefly, we argue that typical duality groups such as SL(2,Z) have sign ambiguities in their actions on fermions, and propose that pertinent duality groups be extended by Z_2, to groups such as the metaplectic group. Specifically, we look at duality groups arising from mapping class groups of tori in M theory compactifications, T-duality, ten-dimensional type IIB S-duality, and (briefly) four-dimensional N=4 super Yang-Mills, and in each case, propose that the full duality group is a nontrivial Z_2 extension of the duality group acting on bosonic degrees of freedom, to more accurately describe possible actions on fermions. We also walk through U-duality groups for toroidal compactifications to nine, eight, and seven dimensions, which enables us to perform cross-consistency tests of these proposals.

Microscopic model of quantum butterfly effect: Out-of-time-order correlators and traveling combustion waves

We extend the Keldysh technique to enable the computation of out-of-time order correlators such as 〈O(t)Õ(0)O(t)Õ(0)〉. We show that the behavior of these correlators is described by equations that display initially an exponential instability which is followed by a linear propagation of the decoherence between two initially identically copies of the quantum many body systems with interactions. At large times the decoherence propagation (quantum butterfly effect) is described by a diffusion equation with non-linear dissipation known in the theory of combustion waves. The solution of this equation is a propagating non-linear wave moving with constant velocity despite the diffusive character of the underlying dynamics.Our general conclusions are illustrated by the detailed computations for the specific models describing the electrons interacting with bosonic degrees of freedom (phonons, two-level-systems etc.) or with each other.

Edwards polaron formation : From one to three dimensions

Employing a self-consistent (optimized) variational diagonalization scheme, we investigate the formation of polaronic quasiparticles in a spinless fermion-boson transport model that couples the movement of charge carriers to fluctuations and correlations of a background medium. The background is parameterized by bosonic degrees of freedom. The variational fermion-boson Hilbert space is constructed to achieve high accuracy in one to three spatial dimensions with modest computational requirements. To characterize the ground-state properties of the Edwards model in the single-particle sector, we present exact numerical results for the polaron band dispersion, quasiparticle weight, Drude weight, mass enhancement, and the particle-boson correlations in a wide parameter regime. In the Edwards model, transport will be quasifree, diffusive or boson-assisted in the weakly fermion-boson coupled, fluctuation-dominated or strongly correlated regimes, respectively. Thereby correlated transport is not only assisted but also limited by the bosonic excitations. As a result, the Drude weight remains finite even in the limit of very small boson frequencies. For a strongly correlated background, closed loops are important, in any dimension, to generate a finite effective particle mass even when the free fermion has an infinite mass.

Quantum phase transitions between bosonic symmetry-protected topological states without sign problem: Nonlinear sigma model with a topological term

We propose a series of simple $2d$ lattice interacting fermion models that we demonstrate at low energy describe bosonic symmetry protected topological (SPT) states and quantum phase transitions between them. This is because due to interaction the fermions are gapped both at the boundary of the SPT states and at the bulk quantum phase transition, thus these models at low energy can be described completely by bosonic degrees of freedom. We show that the bulk of these models is described by a Sp($N$) principal chiral model with a topological $\Theta$-term, whose boundary is described by a Sp($N$) principal chiral model with a Wess-Zumino-Witten term at level-1. The quantum phase transition between SPT states in the bulk is tuned by a particular interaction term, which corresponds to tuning $\Theta$ in the field theory, and the phase transition occurs at $\Theta = \pi$. The simplest version of these models with $N=1$ is equivalent to the familiar O(4) nonlinear sigma model (NLSM) with a topological term, whose boundary is a $(1+1)d$ conformal field theory with central charge $c = 1$. After breaking the O(4) symmetry to its subgroups, this model can be viewed as bosonic SPT states with U(1), or $Z_2$ symmetries, etc. All these fermion models including the bulk quantum phase transitions can be simulated with determinant Quantum Monte Carlo method without the sign problem. Recent numerical results strongly suggests that the quantum disordered phase of the O(4) NLSM with precisely $\Theta = \pi$ is a stable $(2+1)d$ conformal field theory (CFT) with gapless bosonic modes.