Energy Gap Closes Research Articles

Critical non-Hermitian topology induced quantum sensing

Non-Hermitian (NH) physics predicts open quantum system dynamics with unique topological features such as exceptional points and the NH skin effect. We show that this new paradigm of topological systems can serve as probes for bulk Hamiltonian parameters with quantum-enhanced sensitivity reaching Heisenberg scaling. Such enhancement occurs close to a spectral topological phase transition, where the entire spectrum undergoes a delocalization transition. We provide an explanation for this enhanced sensitivity based on the closing of point gap, which is a genuinely NH energy gap with no Hermitian counterpart. This establishes a direct connection between energy-gap closing and quantum enhancement in the NH realm. Our findings are demonstrated through several paradigmatic NH topological models in various dimensions and potential experimental implementations.

Faraday rotation and transmittance as markers of topological phase transitions in 2D materials

We analyze the magneto-optical conductivity (and related magnitudes like transmittance and Faraday rotation of the irradiated polarized light) of some elemental two-dimensional Dirac materials of group IV (graphene analogues, buckled honeycomb lattices, like silicene, germanene, stannane, etc.), group V (phosphorene), and zincblende heterostructures (like HgTe/CdTe quantum wells) near the Dirac and gamma points, under out-of-plane magnetic and electric fields, to characterize topological-band insulator phase transitions and their critical points. We provide plots of the Faraday angle and transmittance as a function of the polarized light frequency, for different external electric and magnetic fields, chemical potential, HgTe layer thickness and temperature, to tune the material magneto-optical properties. We have shown that absortance/transmittance acquires extremal values at the critical point, where the Faraday angle changes sign, thus providing fine markers of the topological phase transition. In the case of non-topological materials as phosphorene, a minimum of the transmittance is also observed due to the energy gap closing by an external electric field.

Ab-initio simulations of coherent phonon-induced pumping of carriers in zirconium pentatelluride

Laser-driven coherent phonons can act as modulated strain fields and modify the adiabatic ground state topology of quantum materials. Here we use time-dependent first-principles and effective model calculations to simulate the effect of the coherent phonon induced by strong terahertz electric field on electronic carriers in the topological insulator ZrTe5. We show that a coherent A1g Raman mode modulation can effectively pump carriers across the band gap, even though the phonon energy is about an order of magnitude smaller than the equilibrium band gap. We reveal the microscopic mechanism of this effect which occurs via Landau–Zener-Stückelberg tunneling of Bloch electrons in a narrow region in the Brillouin zone center where the transient energy gap closes when the system switches from strong to weak topological insulator. The quantum dynamics simulation results are in excellent agreement with recent pump-probe experiments in ZrTe5 at low temperature.

Quantum Simulation of Topological Zero Modes on a 41-Qubit Superconducting Processor.

Quantum simulation of different exotic topological phases of quantum matter on a noisy intermediate-scale quantum (NISQ) processor is attracting growing interest. Here, we develop a one-dimensional 43-qubit superconducting quantum processor, named Chuang-tzu, to simulate and characterize emergent topological states. By engineering diagonal Aubry-André-Harper (AAH) models, we experimentally demonstrate the Hofstadter butterfly energy spectrum. Using Floquet engineering, we verify the existence of the topological zero modes in the commensurate off-diagonal AAH models, which have never been experimentally realized before. Remarkably, the qubit number over 40 in our quantum processor is large enough to capture the substantial topological features of a quantum system from its complex band structure, including Dirac points, the energy gap's closing, the difference between even and odd number of sites, and the distinction between edge and bulk states. Our results establish a versatile hybrid quantum simulation approach to exploring quantum topological systems in the NISQ era.

Quantum phase transitions in the triangular coupled-top model

We study the coupled-top model with three large spins located on a triangle. Depending on the coupling strength, there exist three phases: disordered paramagnetic phase, ferromagnetic phase, and frustrated antiferromagnetic phase, which can be distinguished by the mean-field approach. The paramagnetic-ferromagnetic phase transition is accompanied by the breaking of the global ${Z}_{2}$ symmetry, whereas the paramagnetic-antiferromagnetic phase transition is accompanied by the breaking of both the global ${Z}_{2}$ symmetry and the translational symmetry. Exact analytical results of higher-order quantum effects beyond the mean-field contribution, such as the excitation energy, quantum fluctuation, and von Neumann entropy, can be achieved by the Holstein-Primakoff transformation and symplectic transformation in the thermodynamic limit. Near the quantum critical point, the energy gap closes, along with the divergence of the quantum fluctuation in certain quadrature and von Neumann entropy. Particular attention should be paid to the antiferromagnetic phase, where geometric frustration takes effect. The critical behaviors in the antiferromagnetic phase are quite different from those in the paramagnetic and ferromagnetic phases, which highlight the importance of geometric frustration. The triangular coupled-top model provides a simple and feasible platform to study the quantum phase transition and the novel critical behaviors induced by geometric frustration.

Universal characteristics of one-dimensional non-Hermitian superconductors

We establish a non-Bloch band theory for one-dimensional(1D) non-Hermitian topological superconductors. The universal physical properties of non-Hermitian topological superconductors are revealed based on the theory. According to the particle-hole symmetry, there exist reciprocal particle and hole loops of generalized Brillouin zone. The critical point of quantum phase transition, where the energy gap closes, appears when the particle and hole loops intersect at Bloch points. If the non-Hermitian system has non-Hermitian skin effects, the non-Hermitian skin effect should be the Z 2 skin effect: the corresponding eigenstates of particle and hole localize at opposite ends of an open chain, respectively. The non-Bloch band theory is applied to two examples, non-Hermitian p- and s-wave topological superconductors. In terms of Majorana Pfaffian, a Z 2 non-Bloch topological invariant is defined to establish the non-Hermitian bulk-boundary correspondence for the non-Hermitian topological superconductors.

Geometric quantum adiabatic methods for quantum chemistry

Quantum algorithms have been successfully applied in quantum chemistry to obtain the ground-state energy of small molecules. Although accurate near the equilibrium geometry, the results can become unreliable when the chemical bonds are broken at large distances. For any adiabatic approach, this is usually caused by serious issues, such as energy gap closing or level crossing along the adiabatic evolution path. In this work, we propose a quantum algorithm based on adiabatic evolution to obtain molecular eigenstates and eigenenergies in quantum chemistry, which exploits a smooth geometric deformation by continuously varying bond lengths and bond angles. We demonstrate its utility in several examples on a noiseless quantum simulator, including ${\mathrm{H}}_{2}\mathrm{O}, {\mathrm{CH}}_{2}$, and a chemical reaction of ${\mathrm{H}}_{2}+{\mathrm{D}}_{2}\ensuremath{\rightarrow}$ 2HD, by uniformly stretching chemical bonds. We find that this new algorithm solves the problems related to energy gap closing and level crossing along the adiabatic evolution path at large atomic distances. The new method performs more stably and achieves better accuracy than our previous adiabatic method [Yu and Wei, Phys. Rev. Research 3, 013104 (2021)]. Furthermore, our fidelity analysis demonstrates that even with finite bond length changes, our algorithm still achieves high fidelity for the ground state.

Large Chern-number topological superfluids in a coupled-layer system

We investigate the topological phase transition with large Chern number in a coupled layer system. The topological transitions between different topological superfluids can be realized by controlling the binding energy, interlay tunneling and layer asymmetry {\it etc}. These topological phase transitions can be characterized by energy gap closing and reopening at the critical points at zero momentum, where the Pfaffian and Chern number undergo a discontinuous change. The bulk-edge correspondence ensures that the number of edge modes exactly equals the Chern number. However all these edge modes localized at the same edge have the same chirality and propagate along the same direction. These topological phases can be detected by spin texture at or near zero momentum, which changes discontinuously across the phase transition point due to band inversion. This model can be easily generalized to multilayer system in which the Chern number equals any positive integer --- similar to that in integer quantum Hall effect --- can be realized. This work paves a new way in the realization of topological superfluids with large Chern number.

Majorana fermion states and fractional flux periodicity in mesoscopicd-wave superconducting loops with spin-orbit interaction

We numerically investigate the spin-orbit (SO) coupling effect on the magnetic flux evolution of energy and supercurrent in mesoscopic $d$-wave superconducting loops by solving the spin-generalized Bogoliubov--de Gennes equations self-consistently. It is found that the energy spectrum splits when the SO interaction is involved and the Majorana zero mode can be realized in the [100] edges of square systems for an appropriate SO coupling strength. Superconducting phase transitions appear when the energy gap closes, accompanied by energy jumps between different energy parabolas in the ground state, which provides a possible mechanism to support fractional flux periodicity of supercurrent. Moreover, in the case of rectangular loops with SO coupling, the jumps of the ground-state energy gradually disappear by increasing the ratio of length to height of the sample, and a paramagnetic response with opposite direction of the screening current around zero flux value can occur in such systems.

Density-functional-theory investigation of pressure induced semiconductor–metal transitions in the ferromagnetic semiconductor HgCr2Se4

We investigate the electronic structures of the ferromagnetic semiconductor HgCr2Se4 by using a modified Becke and Johnson exchange potential. The energy gap calculated with the experimental lattice structure is in good agreement with the experimental value. When the pressure reaches 9.0 GPa, HgCr2Se4 becomes a so-called spin gapless semiconductor due to the closure of the spin non-conservation energy gap, and when the pressure increases to 11.4 GPa, the spin conservation energy gap closes, leading to a semiconductor–semimetal transition.

Spin Excitations in an Anisotropic Bond-Alternating QuantumS=1Chain in a Magnetic Field: Contrast to Haldane Spin Chains

Inelastic neutron scattering experiments on the S = 1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependence of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q(parallel) = pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev, Phys. Rev. B 68, 134438 (2003)].

Criticality of the uniform magnetic order in a ferromagnetic-antiferromagnetic random alternating quantum spin chain

An $S=1/2$ ferromagnetic (F) - antiferromagnetic (AF) random alternating Heisenberg quantum spin chain model is investigated in connection to its realization compound: (CH$_3$)$_2$CHNH$_3$Cu(Cl$_x$Br$_{1-x}$)$_3$. The exchange interaction bonds have alternating strong F-AF random bonds and weak uniform AF bonds. Using the quantum Monte Carlo method we have found that the excitation energy gap closes and the uniform AF order becomes critical in the intermediate concentration region. This finding explains the experimental observation of the magnetic transition by considering weak interchain interactions. Present results suggest that the uniform AF order survives even in the presence of randomly located ferromagnetic bonds. This may be a new quantum effect.

Magnetic Excitation in an Anisotropic Bond-AlternatingS= 1 One Dimensional Antiferromagnet Ni(C9D24N4)(NO2)ClO4

We report the results of inelastic neutron scattering (INS) experiments on the S = 1 bond-alternating quasi-one-dimensional (1D) antiferromagnet Ni(C 9 D 24 N 4 )(NO 2 )ClO 4 under magnetic' fields below and above the critical field H c at which the energy gap closes. Normal field dependence of Zeeman split of the excited triplet state below H c has been observed, but the highest mode is unusually small and smears out with increasing field. This is probably explained by the highest branch buried in a magnon continuum, which was never observed in the S = 1 antiferromagnetic uniform chain. Above H c , we observed only one excitation branch, which is completely different from the Haldane material NDMAP [A. Zheludev et al., Phys. Rev. B 68 (2003), 134438] where three gapped branches were clearly observed.

Spin Dynamics of NTENP and NDMAP in Transverse Magnetic Fields

We calculate the field dependence of dynamical structure factors of the S = 1 bond-alternating Heisenberg-chain compound Ni(C 9 D 24 N 4 )(NO 2 )ClO 4 and the S = 1 Haldane-gap compound Ni(C 5 Di 4 N 2 ) 2 N 3 (PF 6 ). We show that in the former system the highest magnon branch vanishes at H ∼ 0.63H c and one gapped branch emerges in H > H c , where H c is the critical field for the energy-gap closing. In the latter system, by contrast, three distinct magnon branches appear below and above H c . The results are in qualitative agreement with recent experimental findings.

Self-Consistent Perturbational Study of Insulator-to-Metal Transition in Kondo Insulators due to Strong Magnetic Field

In order to study the effects of strong magnetic field on Kondo insulators, we calculate magnetization curves and single-particle excitation spectra of the periodic Anderson model at half-filling under finite magnetic field by using the self-consistent second-order perturbation theory combined with the local approximation which becomes exact in the limit of infinite spatial dimensions. Without magnetic field, the system behaves as an insulator with an energy gap, describing the Kondo insulators. By applying magnetic field to f-electrons, we found that the energy gap closes and the first order transition from insulator to metal takes place at a critical field H c . The magnetization curve shows a jump at H c . These are consistent with our previous study in terms of the exact diagonalization. Relationship to the experiments on YbB 12 and some other Kondo insulators is discussed.

Field-induced spin density wave and quantum Hall effect in (TMTSF) 2X

The sign reversal phenomenon of the quantized Hall conductance observed in (TMTSF) 2 X is explained theoretically in terms of the mean field solution for the field-induced spin density wave (FISDW) characterized by many-order parameters (MOP). The many competing OPs can make the sign of the Hall constant change particularly near the subphase boundary. It is shown that the jump of the Hall constant is accompanied by the energy gap closing of the FISDW.