From Ising Model to Kitaev Chain

Quantum coherence will undoubtedly play a fundamental role in understanding of the dynamics of quantum many-body systems, thereby to reveal its genuine contribution is of great importance. In this paper, we specialize our discussions to the one-dimensional transverse field quantum Ising model initialized in the coherent Gibbs state. After quenching the strength of the transverse field, the effects of quantum coherence are studied by the rate function of quantum work distribution. We find that quantum coherence not only recovers the quantum phase transition destroyed by thermal fluctuations, but also generates some entirely new singularities both in the static state and dynamics. It can be manifested that these singularities are rooted in spin flips causing the sudden change of the domain boundaries of spin polarization. This work sheds new light on the fundamental connection between quantum critical phenomena and quantum coherence.

Motivated by the recent experimental realization of minimal Kitaev chains using quantum dots, we investigate the Majorana zero modes (MZM) in Y-shape Kitaev wires. We solve the associated Kitaev models analytically at the sweet spot (th = Δ) and derive the exact form of MZM wave-functions in this geometry. We observed exotic multi-site MZMs located near the junction center, on the nearby edge sites of each leg. This result is important for potential braiding of Majoranas and the performance of Y-junctions made from arrays of quantum dots. Furthermore, we study the stability of local (single-site) and multi-site MZMs modes in the presence of Coulomb repulsion, using density matrix renormalization group theory. Our local density-of-states calculation shows that these multi-site MZMs are as equally topologically protected as the single-site MZMs when in the presence of Coulomb repulsion or when away from the sweet-spot.

We study electrical, thermal and thermoelectric transport in a hybrid device consisting of a long-range Kitaev (LRK) chain coupled to two metallic leads at two ends. Electrical and thermal currents are calculated in this device under both voltage and thermal bias conditions. We find that the transport characteristics of the LRK chain are distinguishably different from its short-range counterpart, which is well known for hosting zero energy Majorana edge modes under some specific range of values of the model parameters. The emergence of massive Dirac fermions, the absence of gap closing at the topological phase transition point and some special features of the energy spectrum which are unique to the LRK chain, significantly alter electrical/thermal current vs. voltage/temperature bias characteristics in comparison with that of the short-range Kitaev chain. These novel transport characteristics of the LRK model can be helpful in understanding nontrivial topological phases of the LRK chain.

The Photonnusber eigenstate (PNE state) generated in a oneatos sphoton sicrolaser systes via the atosic seasuresent for the outofresonance case is shown. The effect of detuning on the probability of obtaining state after having k atoss passed the cavity is discussed. THEORY A beau of lowdensity twolevel atoss is injected into ahighQ cavity at such a low rate that at lost one atos at a t lie is present inside the cay i ty. The cavi ty loss is negi igible. Consider a twolevel atos interacting with a singlesode field via the iphoton transition for the near ly resonant case. The effect i ye Has i lton ian for th is systes in the RWA is Hf cact + q/2)+i1 A q/2+t1g( a'' cy. . Q" ( 1) where L(. )i() is the detuning and ''fi is the energy difference between the two levels of atos g is the iphoton transition atosfield coupling constant Q and *'' are the annihilation and creation operators of the field and ca is the frequency of field a3 and a. are the Pauli spin operators. Assuse that the field is in PNE state at a tue t1 in which the ith excited atol is just going to be injected. r is the tile for the ith atoi to pass through the cavity. The density operator p (t+t ) is p (t+t )U( i: ) p

Silicene is a monolayer honeycomb system made of silicon. It is a two-dimensional topological insulator that undergoes a topological phase transition to a band insulator by applying an external electromagnetic field. All topological phase transitions in silicene come by tuning of its Dirac mass. In this paper, the tuning of the Dirac mass of silicene has been done by the application of Floquet theory. The nature of the Dirac mass in a Bloch–Seigert shift is shown in topological trivial and non-trivial phases of silicene. The collapse-revival spectra have been described by Floquet theory in silicene. The differential transmission coefficient of pump–probe spectra is shown, which have the capability of distinguishing Floquet theory oscillations in topological trivial and non-trivial phases of silicene. All these results are also valid for germanene and stanene by changing the material parameters.

We study an inhomogeneous critical Ising chain in a transverse field whose couplings decay exponentially from the center. In the strong inhomogeneity limit, we apply Fisher's renormalization group to show that the ground state is formed by concentric singlets similar to those of the rainbow state of the XX model. In the weak inhomogeneity limit, we map the model to a massless Majorana fermion living in a hyperbolic space-time, where, using conformal field theory techniques, we derive the entanglement entropy and show that it presents a linear scaling. We also study an inhomogeneous noncritical Ising model that for weak inhomogeneity is mapped to a massive Majorana fermion, while for strong inhomogeneity regime, it exhibits trivial and nontrivial topological phases and a separation between regions with high and low entanglement. We also present the entanglement Hamiltonian of the model.

We study the effects of Lorentz transformations on three-particle non-local system states (GHZ and W) of spin 1/2 particles, using the Pauli spin operator and a three-particle generalization of Bell's inequality, introduced by Svetlichny. In our setup, the moving and laboratory frames used the (same) set of measurement directions that maximally violate Svetlichny's inequality in the laboratory frame. We also investigate the behavior of Mermin's and Collins' inequalities. We find that, regardless of the particles' type of entanglement, violation of Svetlichny's inequality in the moving frame is decreased by increasing the boost velocity and the energy of particles in the laboratory frame. In the relativistic regime Svetlichny's inequality is a good criterion to investigate the non-locality of the GHZ state. We also find that Mermin's and Collins' inequalities lead to reasonable predictions, in agreement with the behavior of the spin state, about non-locality of the W state in the relativistic regime. Then, comparing our results with those in which Czachor's relativistic spin is used instead of the Pauli operator, we find that the results obtained by considering the Pauli spin operator are in better agreement with the behavior of spin state of the system in the relativistic information theory.

Majorana fermions, exotic particles with potential applications in quantum computing, have garnered significant interest in condensed matter physics. The Kitaev model serves as a fundamental framework for investigating the emergence of Majorana fermions in one-dimensional systems. We explore the intriguing question of whether Majorana fermions can arise in a normal metal (NM) side-coupled to a Kitaev chain (KC) in the topologically trivial phase. Our findings reveal affirmative evidence, further demonstrating that the KC, when in the topological phase, can induce additional Majorana fermions in the neighboring NM region. Through extensive parameter analysis, we uncover the potential for zero, one, or two pairs of Majorana fermions in a KC side-coupled to an NM. Additionally, we investigate the impact of magnetic flux on the system and calculate the winding number -a topological invariant used to characterize topological phases.

Although non-commutativity of a certain set of quantum operators (e.g.,\ncreation/annihilation operators and Pauli spin operators) has been shown\nexperimentally in recent years, the commu- tation relation for the position and\nthe momentum operators has not been directly demonstrated to date. In this\npaper, we propose and analyze an experimental scheme for directly observing the\nnon-commutativity of the position and the momentum operators using\nsingle-photon quantum in- terference. While the scheme is studied for the\nsingle-photon state as the input quantum state, the analysis applies equally to\nmatter-wave interference, allowing a direct test of the position-momentum\ncommutation relation with a massive particle.\n

We propose a physical witness for dynamically detecting topological phase transitions (TPTs) via an experimentally observable out-of-time-order correlation (OTOC). The distinguishable OTOC dynamics appears in the topological trivial and non-trivial phases due to the topological locality. In the long-time limit, the OTOC undergoes a {\it zero-to-finite-value transition} at the critical point of the TPTs. This transition is robust to the choices of the initial state of the system and the used operators in OTOC. The proposed OTOC witness can be applied into the systems with and without chiral symmetry, e.g., the lattices described by the SSH model, Creutz model, and Haldane model. Moreover, our proposal, as a physical witness in real space, is still valid even in the presence of disorder. Our work fundamentally offers a new prospect of exploring topological physics with quantum correlations.

We have developed a mirrored photonic crystal interface (MPCI) by applying a mirror operator to expanded honeycomb photonic crystals (EHPCs) exhibiting nontrivial band topology. This configuration supports a pair of interface states characterized by spin-momentum locking. Notably, by adjusting the geometric parameters of the EHPCs without altering their topological properties, we observe a process where these interface states close and reopen, indicating a topological phase transition. Further analysis reveals that the MPCIs function as interfaces between EHPCs with C6- and C3-symmetric configurations, representing nontrivial and trivial topological phases, respectively, separated by air gaps. Our findings highlight the tunable nature of topological edge states formed by a single type of photonic crystal, which could have potential applications in robust transport devices within photonic integrated circuits.

We discuss how nonlocality originates in long-range quantum systems and how it affects their dynamics at and out of equilibrium. We focus in particular on the Kitaev chains with long-range pairings and on the quantum Ising chain with long-range antiferromagnetic coupling (both having a power-law decay with exponent α). By studying the dynamic correlation functions, we find that for every finite α two different behaviours can be identified, one typical of short-range systems and the other connected with locality violation. The latter behaviour is shown related also with the known power-law decay tails previously observed in the static correlation functions, and originated by modes—having in general energies far from the minima of the spectrum—where particular singularities develop as a consequence of the long-rangedness of the system. We refer to these modes as to ‘singular’ modes, and as to ‘singular dynamics’ to their dynamics. For the Kitaev model they are manifest, at finite α, in derivatives of the quasiparticle energy, the order of the derivatives at which the singularity occurs is increasing with α. The features of the singular modes and their physical consequences are clarified by studying an effective theory for them and by a critical comparison of the results from this theory with the lattice ones. Moreover, a numerical study of the effects of the singular modes on the time evolution after various types of global quenches is performed. We finally present and discuss the presence of singular modes and their consequences in interacting long-range systems by investigating in the long-range Ising quantum chain, both in the deep paramagnetic regime and at criticality, where they also play a central role for the breakdown of conformal invariance.

Recent experiments using the quantum dot coupled to the topological superconducting nanowire [M.T. Deng et al., Science 354, 1557 (2016)}] revealed that zero-energy bound state coalesces from the Andreev bound states. Such quasiparticle states, present in the quantum dot, can be controlled by the magnetic and electrostatic means. We use microscopic model of the quantum-dot--nanowire structure to reproduce the experimental results, applying the Bogoliubov--de~Gennes technique. This is done by studying the gate voltage dependence of the various types of bound states and mutual influence between them. We show that the zero energy bound states can emerge from the Andreev bound states in topologically trivial phase and can be controlled using various means. In non-trivial topological phase we show the possible resonance between this zero energy levels with Majorana bound states. We discuss and explain this phenomena as a result of dominant spin character of discussed bound states. Presented results can be applied in experimental studies by using the proposed nanodevice.

A theory for light-induced current by strong optical pulses in molecular tunneling junctions is described. We consider a molecular bridge represented by its highest occupied and lowest unoccupied levels. We take into account two types of couplings between the molecule and the metal leads: electron transfer that gives rise to net current in the biased junction and energy transfer between the molecule and electron-hole excitations in the leads. Using a Markovian approximation, we derive a closed system of equations for the expectation values of the relevant variables: populations and molecular polarization that are binary, and exciton populations that are tetradic in the annihilation and creation operators for electrons in the molecular states. We have proposed an optical control method using chirped pulses for enhancing charge transfer in unbiased junctions where the bridging molecule is characterized by a strong charge-transfer transition. An approximate analytical solution of the resulting dynamical equations is supported by a full numerical solution. When energy transfer between the molecule and electron-hole excitations in the leads is absent, the optical control problem for inducing charge transfer with a linearly chirped pulse can be reduced to the Landau-Zener transition to a decaying level. When the chirp is fast with respect to the rate of the electron transfer, the Landau theory is recovered. The proposed control mechanism is potentially useful for developing optoelectronic single-electron devices with optical gating based on molecular nanojunctions.

The Ising chain in transverse field is a paradigmatic model for a host of physical phenomena, including spontaneous symmetry breaking, topological defects, quantum criticality, and duality. Although the quasi-1D ferromagnet CoNb$_2$O$_6$ has been put forward as the best material example of the transverse field Ising model, it exhibits significant deviations from ideality. Through a combination of THz spectroscopy and theory, we show that CoNb$_2$O$_6$ in fact is well described by a different model with strong bond dependent interactions, which we dub the {\it twisted Kitaev chain}, as these interactions share a close resemblance to a one-dimensional version of the intensely studied honeycomb Kitaev model. In this model the ferromagnetic ground state of CoNb$_2$O$_6$ arises from the compromise between two distinct alternating axes rather than a single easy axis. Due to this frustration, even at zero applied field domain-wall excitations have quantum motion that is described by the celebrated Su-Schriefer-Heeger model of polyacetylene. This leads to rich behavior as a function of field. Despite the anomalous domain wall dynamics, close to a critical transverse field the twisted Kitaev chain enters a universal regime in the Ising universality class. This is reflected by the observation that the excitation gap in CoNb$_2$O$_6$ in the ferromagnetic regime closes at a rate precisely twice that of the paramagnet. This originates in the duality between domain walls and spin-flips and the topological conservation of domain wall parity. We measure this universal ratio `2' to high accuracy -- the first direct evidence for the Kramers-Wannier duality in nature.