Fermionic Modes Research Articles

Modified supersymmetric indices in AdS3/CFT2

We consider the \U0001d4a9 = (2, 2) AdS3/CFT2 dualities proposed by Eberhardt, where the bulk geometry is AdS3 × (S3 × T4)/ℤk, and the CFT is a deformation of the symmetric orbifold of the supersymmetric sigma model T4/ℤk (with k = 2, 3, 4, 6). The elliptic genera of the two sides vanish due to fermionic zero modes, so for microstate counting applications one must consider modified supersymmetric indices. In an analysis similar to that of Maldacena, Moore, and Strominger for the standard \U0001d4a9 = (4, 4) case of T4, we study the appropriate helicity-trace index of the boundary CFTs. We encounter a strange phenomenon where a saddle-point analysis of our indices reproduces only a fraction (respectively 12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document}, 23\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{2}{3} $$\\end{document}, 34\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{3}{4} $$\\end{document}, 56\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{5}{6} $$\\end{document}) of the Bekenstein-Hawking entropy of the associated macroscopic black branes.

Probability measures of fermions on branes

In our research, we explore the impact of a geometric non-minimal coupling between fermions and curvature scalars on the positioning of fermions within a brane structure. Our investigation encompasses massless fermionic modes and massive modes, revealing that specifically fermionic modes with left chirality are situated within the brane. This insight allows us to gain a more direct understanding of how the system’s geometry influences the placement of fermion fields on the brane. To delve deeper into the precise localization of massless fermionic modes, we employ entropic information measurements. By varying the parameters that govern the curvature scalars, we observe the ability to adjust the localization of these fermionic modes on the brane. Importantly, the BBM uncertainty relation remains satisfied in all scenarios, particularly for f1,2,3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{1,2,3}$$\\end{document}. We leverage the Shannon entropy as a highly effective metric to yield accurate results regarding the positioning of massless fermionic modes within our model. In the case of massive fermionic modes, we utilize relative probability analysis to pinpoint the resonant modes, and we identify the existence of these resonant modes in both f1,2,3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{1,2,3}$$\\end{document} cases. Ultimately, we ascertain that these parameters influence the placement of resonant modes by increasing the amplitude of the massive modes in the core of the brane.

A nontopological soliton in an [formula omitted] supersymmetric Abelian gauge model

A version of N=1 supersymmetric scalar electrodynamics is considered here, and it is shown that an electrically charged nontopological soliton exists in this model. In addition to the long-range electric field, the soliton also possesses a long-range scalar field, which leads to a modification of the intersoliton interaction potential at large distances. The supersymmetry of the model makes it possible to express fermionic zero modes of the soliton in terms of bosonic fields. The properties of the nontopological soliton are investigated using analytical and numerical methods.

Finite-time Landauer principle beyond weak coupling

Landauer's principle gives a fundamental limit to the thermodynamic cost of erasing information. Its saturation requires a reversible isothermal process, and hence infinite time. We develop a finite-time version of Landauer's principle for a bit encoded in the occupation of a single fermionic mode, which can be strongly coupled to a reservoir. By solving the exact non-equilibrium dynamics, we optimize erasure processes (taking both the fermion's energy and system-bath coupling as control parameters) in the slow driving regime through a geometric approach to thermodynamics. We find analytic expressions for the thermodynamic metric and geodesic equations, which can be solved numerically. Their solution yields optimal processes that allow us to characterize a finite-time correction to Landauer's bound, fully taking into account non-markovian and strong coupling effects.

Discovering optimal fermion-qubit mappings through algorithmic enumeration

Simulating fermionic systems on a quantum computer requires a high-performing mapping of fermionic states to qubits. A characteristic of an efficient mapping is its ability to translate local fermionic interactions into local qubit interactions, leading to easy-to-simulate qubit Hamiltonians.All fermion-qubit mappings must use a numbering scheme for the fermionic modes in order for translation to qubit operations. We make a distinction between the unordered labelling of fermions and the ordered labelling of the qubits. This separation shines light on a new way to design fermion-qubit mappings by making use of the enumeration scheme for the fermionic modes. The purpose of this paper is to demonstrate that this concept permits notions of fermion-qubit mappings that are optimal with regard to any cost function one might choose. Our main example is the minimisation of the average number of Pauli matrices in the Jordan-Wigner transformations of Hamiltonians for fermions interacting in square lattice arrangements. In choosing the best ordering of fermionic modes for the Jordan-Wigner transformation, and unlike other popular modifications, our prescription does not cost additional resources such as ancilla qubits.We demonstrate how Mitchison and Durbin's enumeration pattern minimises the average Pauli weight of Jordan-Wigner transformations of systems interacting in square lattices. This leads to qubit Hamiltonians consisting of terms with average Pauli weights 13.9% shorter than previously known. By adding only two ancilla qubits we introduce a new class of fermion-qubit mappings, and reduce the average Pauli weight of Hamiltonian terms by 37.9% compared to previous methods. For n-mode fermionic systems in cellular arrangements, we find enumeration patterns which result in n1/4 improvement in average Pauli weight over naïve schemes.

Quench dynamics of edge states in a finite extended Su-Schrieffer-Heeger system.

We examine the quench dynamics of an extended Su-Schrieffer-Heeger (SSH) model involving long-range hopping that can hold multiple topological phases. Using winding number diagrams to characterize the system's topological phases geometrically, it is shown that there can be multiple winding number transition paths for a quench between two topological phases. The dependence of the quench dynamics is studied in terms of the survival probability of the fermionic edge modes and postquench transport. For two quench paths between two topological regimes with the same initial and final topological phase, the survival probability of edge states is shown to be strongly dependent on the winding number transition path. This dependence is explained using energy band diagrams corresponding to the paths. Following this, the effect of the winding number transition path on transport is investigated. We find that the velocities of maximum transport channels varied along the winding number transition path. This variation depends on the path we choose, i.e., it increases or decreases depending upon the path. An analysis of the coefficient maps, energy spectrum, and spatial structure of the edge states of the final quench Hamiltonian provides an understanding of the path-dependent velocity variation phenomenon.

Transforming collections of Pauli operators into equivalent collections of Pauli operators over minimal registers

Transformations which convert between fermionic modes and qubit operations have become a ubiquitous tool in quantum algorithms for simulating systems. Similarly, collections of Pauli operators might be obtained from solutions of nonlocal games and satisfiability problems. Drawing on ideas from entanglement-assisted quantum error-correcting codes and quantum convolutional codes, we prove the obtainable lower bound for the number of qubits needed to represent such Pauli operations which are equivalent to the initial ones and provide a procedure for determining such a set of minimal register Pauli operations.

Discovery prospects of a light charged Higgs near the fermiophobic region of Type-I 2HDM

Determining if the SM-like Higgs is part of an extended Higgs sector is the most important question to be asked after discovery. A light charged Higgs boson with mass smaller than the sum of top and bottom quarks is naturally allowed in Type-I two Higgs doublet model and can be produced in association with neutral scalars for large parts of parameter space at the LHC. Such low mass charged scalars typically have dominant decays to the fermionic modes viz. τν and cs. However in the presence of light neutral scalar (φ), the charged Higgs boson has a substantial branching fraction into the bosonic decay modes H±→ W(*)φ. Identifying the heavier neutral Higgs (H) with the observed 125 GeV Higgs and working in the limit {M}_{H^{pm }}approx {M}_A , we examine charged Higgs production and decay in the bosonic mode pp → H±h → W(∗)hh. The presence of two light Higgses (h) is then the key to identifying charged Higgs production. The light Higgs branching ratio is largely dominated by the boverline{b} mode except when close to the fermiophobic limit. Here, the rates into boverline{b} and γγ can be comparable and we can use the gamma gamma boverline{b} signature. This signature is complementary to the hh → 4γ which has been previously discussed in literature. Using the lepton from the W boson, we demonstrate with a cut-and-count analysis that both the new light neutral Higgs as well as charged Higgs can be probed with reasonable significance at 13.6 TeV LHC with 300-3000 fb−1 of integrated luminosity.

Zero modes of fermions trapped by giant vortices

Zero-energy solutions of the Dirac equation for the fermions bound to giant vortices of large winding number n are studied in the abelian Higgs and Chern-Simons Higgs models. The case of Jackiw-Rossi theory of the Majorana states in topological superconductors is discussed in detail. By expanding in inverse powers of n we find an analytic result for asymptotically all n solutions required by the index theorem. In the abelian Higgs model the zero modes fill the vortex core and reveal a universal structure independent of fine details of the gauge and scalar field interactions which, in particular, determines the general properties of the large-n superconducting cosmic strings. On the contrary, for the Chern-Simons Higgs vortices the zero modes are localized on the core boundary and the explicit solution is obtained for the supersymmetric couplings in a self-dual background.

Coupling sum rules and oblique corrections in gauge-Higgs unification

Abstract In grand-unified-theory-inspired SO(5) × U(1)X × SU(3)C gauge-Higgs unification (GHU) in the Randall–Sundrum warped spacetime, the W- and Z-couplings of all 4D fermion modes become nontrivial. The W- and Z-couplings of zero-mode quarks and leptons slightly deviate from those in the SM, and the couplings take the matrix form in the space of Kaluza–Klein (KK) states. In particular, the 4D couplings and mass spectra in the KK states depend on the Aharonov–Bohm phase θH in the fifth dimension. Nevertheless there emerge three astonishing sum rules among those coupling matrices, which guarantees the finiteness of certain combinations of corrections to vacuum polarization tensors. We confirm by numerical evaluation that the equality in the sum rules holds with 5- to 7-digit accuracy. Based on the sum rules we propose improved oblique parameters in GHU. Oblique corrections due to fermion 1-loop diagrams are found to be small.

Geometry-independent tight-binding method for massless Dirac fermions in two dimensions

The Nielsen-Ninomiya theorem, dubbed `fermion-doubling', poses a problem for the naive discretization of a single (massless) Dirac cone on a two-dimensional surface. The inevitable appearance of an additional, unphysical fermionic mode can, for example, be circumvented by introducing an extra dimension to spatially separate Dirac cones. In this work, we propose a geometry-independent protocol based on a tight-binding model for a three-dimensional topological insulator on a cubic lattice. The low-energy theory, below the bulk gap, corresponds to a Dirac cone on its two-dimensional surface which can have an arbitrary geometry. We introduce a method where only a thin shell of the topological insulator needs to be simulated. Depending on the setup, we propose to gap out the states on the undesired surfaces either by breaking the time-reversal symmetry or by introducing a superconducting pairing. We show that it is enough to have a thickness of the topological-insulator shell of three to nine lattice constants. This leads to an effectively two-dimensional scaling with minimal and fixed shell thickness. We test the idea by comparing the spectrum and probability distribution to analytical results for both a proximitized Dirac mode and a Dirac mode on a sphere which exhibits a nontrivial spin-connection. The protocol yields a tight-binding model on a cubic lattice simulating Dirac cones on arbitrary surfaces with only a small overhead due to the finite thickness of the shell.

Supersymmetric indices factorize

The extent to which quantum mechanical features of black holes can be understood from the Euclidean gravity path integral has recently received significant attention. In this paper, we examine this question for the calculation of the supersymmetric index. For concreteness, we focus on the case of charged black holes in asymptotically flat four-dimensional mathcal{N} = 2 ungauged supergravity. We show that the gravity path integral with supersymmetric boundary conditions has an infinite family of Kerr-Newman classical saddles with different angular velocities. We argue that fermionic zero-mode fluctuations are present around each of these solutions making their contribution vanish, except for a single saddle that is BPS and gives the expected value of the index. We then turn to non-perturbative corrections involving spacetime wormholes and show that a fermionic zero mode is present in all these geometries, making their contribution vanish once again. This mechanism works for both single- and multi-boundary path integrals. In particular, only disconnected geometries without wormholes contribute to the gravitational path integral which computes the index, and the factorization puzzle that plagues the black hole partition function is resolved for the supersymmetric index. Finally, we classify all other single-centered geometries that yield non-perturbative contributions to the gravitational index of each boundary.

Recent progress on non-Abelian anyons: from Majorana zero modes to topological Dirac fermionic modes

Majorana zero modes (MZMs) have been intensively studied in recent decades theoretically and experimentally as the most promising candidate for non-Abelian anyons supporting topological quantum computation (TQC). In addition to the Majorana scheme, some non-Majorana quasiparticles obeying non-Abelian statistics, including topological Dirac fermionic modes, have also been proposed and therefore become new candidates for TQC. In this review, we overview the non-Abelian braiding properties as well as the corresponding braiding schemes for both the MZMs and the topological Dirac fermionic modes, emphasizing the recent progress on topological Dirac fermionic modes. A topological Dirac fermionic mode can be regarded as a pair of MZMs related by unitary symmetry, which can be realized in a number of platforms, including the one-dimensional topological insulator, higher-order topological insulator, and spin superconductor. This topological Dirac fermionic mode possesses several advantages compared with its Majorana cousin, such as superconductivity-free and larger gaps. Therefore, it provides a new avenue for investigating non-Abelian physics and possible TQC.

Fermionic One-Body Entanglement as a Thermodynamic Resource.

There is ongoing controversy about whether a coherent superposition of the occupied states of two fermionic modes should be regarded entangled or not, that is, whether its intrinsic quantum correlations are operationally accessible and useful as a resource. This has been questioned on the basis that such an entanglement cannot be accessed by local operations on individual modes due to the parity superselection rule which constrains the set of physical observables. In other words, one cannot observe violations of Bell's inequality. Here, we show, however, that entanglement of a two-mode fermionic state can be used as a genuine quantum resource in open-system thermodynamic processes, enabling one to perform tasks forbidden for separable states. We thus demonstrate that quantum thermodynamics can shed light on the nature of fermionic entanglement and the operational meaning of the different notions used to define it.

Quantum breakdown model: From many-body localization to chaos with scars

We propose a quantum model of fermions simulating the electrical breakdown process of dielectrics. The model consists of $M$ sites with $N$ fermion modes per site, and has a conserved charge $Q$. It has an on-site chemical potential $\mu$ with disorder $W$, and an interaction of strength $J$ restricting each fermion to excite two more fermions when moving forward by one site. We show the $N=3$ model with disorder $W=0$ show a Hilbert space fragmentation and is exactly solvable except for very few Krylov subspaces. The analytical solution shows that the $N=3$ model exhibits many-body localization (MBL) as $M\rightarrow\infty$, which is stable against $W>0$ as our exact diagonalization (ED) shows. At $N>3$, our ED suggests a MBL to quantum chaos crossover at small $W$ as $M/N$ decreases across $1$, and persistent MBL at large $W$. At $W=0$, an exactly solvable many-body scar flat band exists in many charge $Q$ sectors, which has a nonzero measure in the thermodynamic limit. We further calculate the time evolution of a fermion added to the particle vacuum, which shows a breakdown (dielectric) phase when $\mu/J<1/2$ ($\mu/J>1/2$) if $W\ll J$, and no breakdown if $W\gg J$.

Is the right-handed current contribution to B¯→Xulν decays corrected by the nontrivial vacuum in QCD?

We study violation of quark-hadron duality for $\overline{B}\ensuremath{\rightarrow}{X}_{u}l\ensuremath{\nu}$ and $D\ensuremath{\rightarrow}{X}_{d}l\ensuremath{\nu}$ decays in the presence of the right-handed current operator. For this case, we show that duality violation has some aspects different from the standard model due to the existence of an instanton. In particular, the fermionic zero mode of an intermediate light quark can give a nonvanishing contribution owing to its chirality structure. A duality-violating component that arises from a single instanton is then analytically extracted as a finite-distance singularity, leading to an oscillatory correction to the observable in Minkowski space. Finally, we show that the size of duality violation for the lepton energy distribution in $\overline{B}$ decays can be comparable to the chirally suppressed perturbative contribution, although the absolute size depends on the detail of the QCD vacuum.

Stationary states of open XX -spin chains

We study an open quantum spin chain of arbitrary length with nearest neighbor $XX$ interactions of strength $g$, immersed in an external constant magnetic field $\mathrm{\ensuremath{\Delta}}$ along the $z$ direction, whose end spins are weakly coupled to two heat baths at different temperatures. In the so-called global approach, namely, without neglecting interspin interactions, using standard weak-coupling limit techniques, we first derive the open chain master equation written in terms of fermionic mode operators. Then, we focus on the study of the dependence of the resulting open dynamics from the ratio $r\ensuremath{\equiv}g/\mathrm{\ensuremath{\Delta}}$. By increasing $r$, some of the chain Bohr transition frequencies become negative; when this occurs, both the generator of the dissipative time evolution and its stationary states behave discontinuously. As a consequence, the asymptotic spin and heat flows also exhibit discontinuities, but in a different way: while source terms in the spin flow continuity equation show jumps, the heat flow instead is continuous but with discontinuous first derivatives with respect to $r$. These two behaviors might be experimentally accessible; in particular, they could discriminate between the global and the local approaches to open quantum spin chains. Indeed, the latter one, which neglects interspin interactions in the derivation of the master equation, does not show any kind of discontinuous behavior.

Excitation spectra of one-dimensional spin-1/2 Fermi gas with an attraction

Using an exact Bethe ansatz solution, we rigorously study excitation spectra of the spin-1/2 Fermi gas (called Yang–Gaudin model) with an attractive interaction. Elementary excitations of this model involve particle-hole excitation, hole excitation and adding particles in the Fermi seas of pairs and unpaired fermions. The gapped magnon excitations in the spin sector show a ferromagnetic coupling to the Fermi sea of the single fermions. By numerically and analytically solving the Bethe ansatz equations and the thermodynamic Bethe ansatz equations of this model, we obtain excitation energies for various polarizations in the phase of the Fulde–Ferrell–Larkin–Ovchinnikov-like state. For a small momentum (long-wavelength limit) and in the strong interaction regime, we analytically obtained their linear dispersions with curvature corrections, effective masses as well as velocities in particle-hole excitations of pairs and unpaired fermions. Such a type of particle-hole excitations display a novel separation of collective motions of bosonic modes within paired and unpaired fermions. Finally, we also discuss magnon excitations in the spin sector and the application of Bragg spectroscopy for testing such separated charge excitation modes of pairs and single fermions.

Quantifying fermionic nonlinearity of quantum circuits

Variational quantum algorithms (VQAs) have been proposed as one of the most promising approaches to demonstrate quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, it has been unclear whether VQAs can maintain quantum advantage under the intrinsic noise of the NISQ devices, which deteriorates the quantumness. Here we propose a measure, called fermionic nonlinearity, to quantify the classical simulatability of quantum circuits designed for simulating fermionic Hamiltonians. Specifically, we construct a Monte Carlo type classical algorithm based on the classical simulatability of fermionic linear optics, whose sampling overhead is characterized by the fermionic nonlinearity. As a demonstration of these techniques, we calculate the upper bound of the fermionic nonlinearity of a rotation gate generated by four fermionic modes under the dephasing noise. Moreover, we estimate the sampling costs of the unitary coupled cluster singles and doubles quantum circuits for hydrogen chains subject to the dephasing noise. We find that, depending on the error probability and atomic spacing, there are regions where the fermionic nonlinearity becomes very small or unity, and hence the circuits are classically simulatable. We believe that our method and results help to design quantum circuits for fermionic systems with potential quantum advantages.

Tunable Mode Entanglement: Topological Su–Schrieffer–Heeger (SSH) Chain with an Embedded Aharonov–Bohm Quantum Ring

AbstractA variant of the SSH model consisting of an SSH chain with an embedded Aharonov–Bohm quantum ring is investigated. The embedded ring gives rise to domain wall states whose energy levels are in the band gap. The dependence of some of the states on the ring's magnetic flux provides a mechanism to control the entanglement between the two SSH edge fermion modes. The concurrence between the edge modes depends periodically on the magnetic flux. In the deep topological zone, for appropriate values of the flux, the concurrence reaches the extreme values of 0 and 1, corresponding to vanishing entanglement and to maximum entanglement. Therefore, the QR‐SSH system offers a tuning mechanism that can be used either as an entanglement modulator or as an entanglement switch.