Amit Dutta

Bio: Amit Dutta is an academic researcher from Indian Institute of Technology Kanpur. The author has contributed to research in topics: Quantum phase transition & Quantum critical point. The author has an hindex of 24, co-authored 92 publications receiving 1892 citations. Previous affiliations of Amit Dutta include Max Planck Society.

Quantum Phase Transitions in Transverse Field Spin Models: From Statistical Physics to Quantum Information

Abstract: The transverse field Ising and XY models (the simplest quantum spin models) provide the organising principle for the rich variety of interconnected subjects which are covered in this book From a generic introduction to in-depth discussions of the subtleties of the transverse field Ising and related models, it includes the essentials of quantum dynamics and quantum information A wide range of relevant topics has also been provided: quantum phase transitions, various measures of quantum information, the effects of disorder and frustration, quenching dynamics and the Kibble–Zurek scaling relation, the Kitaev model, topological phases of quantum systems, and bosonisation In addition, it also discusses the experimental studies of transverse field models (including the first experimental realisation of quantum annealing) and the recent realisation of the transverse field Ising model using tunable Josephson junctions Further, it points to the obstacles still remaining to develop a successful quantum computer

Floquet generation of Majorana end modes and topological invariants

Abstract: We show how Majorana end modes can be generated in a one-dimensional system by varying some of the parameters in the Hamiltonian periodically in time. The specific model we consider is a chain containing spinless electrons with a nearest-neighbor hopping amplitude, a $p$-wave superconducting term, and a chemical potential; this is equivalent to a spin-$\frac{1}{2}$ chain with anisotropic $XY$ couplings between nearest neighbors and a magnetic field applied in the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ direction. We show that varying the chemical potential (or magnetic field) periodically in time can produce Majorana modes at the ends of a long chain. We discuss two kinds of periodic driving, periodic $\ensuremath{\delta}$-function kicks, and a simple harmonic variation with time. We discuss some distinctive features of the end modes such as the inverse participation ratio of their wave functions and their Floquet eigenvalues which are always equal to $\ifmmode\pm\else\textpm\fi{}1$ for time-reversal-symmetric systems. For the case of periodic $\ensuremath{\delta}$-function kicks, we use the effective Hamiltonian of a system with periodic boundary conditions to define two topological invariants. The first invariant is a well-known winding number, while the second invariant has not appeared in the literature before. The second invariant is more powerful in that it always correctly predicts the numbers of end modes with Floquet eigenvalues equal to $+1$ and $\ensuremath{-}1$, while the first invariant does not. We find that the number of end modes can become very large as the driving frequency decreases. We show that periodic $\ensuremath{\delta}$-function kicks in the hopping and superconducting terms can also produce end modes. Finally, we study the effect of electron-phonon interactions (which are relevant at finite temperatures) and a random noise in the chemical potential on the Majorana modes.

Phase transitions in the quantum Ising and rotor models with a long-range interaction

Abstract: We investigate the zero-temperature and finite-temperature phase transitions of quantum Ising and quantum rotor models. We here assume a long-range (falling off as ${1/r}^{d+\ensuremath{\sigma}},$ where r is the distance between two spins/rotors in units of lattice spacing) ferromagnetic interaction among the spins or rotors. We find that the long-range behavior of the interaction drastically modifies the universal critical behavior of the system. The corresponding upper critical dimension and the hyperscaling relation and exponents associated with the quantum transition are modified and, as expected, they attain values of short-range system when $\ensuremath{\sigma}=2.$ The dynamical exponent varies continuously as the parameter \ensuremath{\sigma} and is unity for $\ensuremath{\sigma}=2.$ The one-dimensional long-range quantum Ising system shows a phase transition at $T=0$ for all values of \ensuremath{\sigma}. The most interesting observation is that the phase diagram for $\ensuremath{\sigma}=d=1$ shows a line of Kosterlitz-Thouless transition at finite temperature even though the $T=0$ transition is a simple order-disorder transition. These finite temperature transitions are studied near the phase boundary using renormalisation group equations and a region with diverging susceptibility is located. We have also studied one-dimensional quantum rotor model which exhibits a rich and interesting transition behavior depending upon the parameter \ensuremath{\sigma}. We explore the phase diagram extending the short-range quantum nonlinear \ensuremath{\sigma} model renormalisation group equations to the present case.

Slow quenches in a quantum Ising chain: Dynamical phase transitions and topology

Abstract: We study the slow quenching dynamics (characterized by an inverse rate ${\ensuremath{\tau}}^{\ensuremath{-}1}$) of a one-dimensional transverse Ising chain with nearest neighbor ferromagentic interactions across the quantum critical point (QCP) and analyze the Loschmidt overlap measured using the subsequent temporal evolution of the final wave function (reached at the end of the quenching) with the final time-independent Hamiltonian. Studying the Fisher zeros of the corresponding generalized ``partition function,'' we probe nonanalyticities manifested in the rate function of the return probability known as dynamical phase transitions (DPTs). In contrast to the sudden quenching case, we show that DPTs survive in the subsequent temporal evolution following the quenching across two critical points of the model for a sufficiently slow rate; furthermore, an interesting ``lobe'' structure of Fisher zeros emerge. We have also made a connection to topological aspects studying the dynamical topological order parameter $[{\ensuremath{ u}}_{D}(t)]$ as a function of time $(t)$ measured from the instant when the quenching is complete. Remarkably, the time evolution of ${\ensuremath{ u}}_{D}(t)$ exhibits drastically different behavior following quenches across a single QCP and two QCPs. In the former case, ${\ensuremath{ u}}_{D}(t)$ increases stepwise by unity at every DPT (i.e., $\mathrm{\ensuremath{\Delta}}{\ensuremath{ u}}_{D}=1$). In the latter case, on the other hand, ${\ensuremath{ u}}_{D}(t)$ essentially oscillates between 0 and 1 (i.e., successive DPTs occur with $\mathrm{\ensuremath{\Delta}}{\ensuremath{ u}}_{D}=1$ and $\mathrm{\ensuremath{\Delta}}{\ensuremath{ u}}_{D}=\ensuremath{-}1$, respectively), except for instants where it shows a sudden jump by a factor of unity when two successive DPTs carry a topological charge of the same sign.

Mixed state dynamical quantum phase transitions

Abstract: Preparing an integrable system in a mixed state described by a thermal density matrix, we subject it to a sudden quench and explore the subsequent unitary dynamics. To address the question of whether the nonanalyticities, namely, the dynamical quantum phase transitions (DQPTs), persist when the initial state is mixed, we consider two versions of the generalized Loschmidt overlap amplitude (GLOA). Our study shows that the GLOA constructed using the Uhlmann approach does not show any signature of DQPTs at any nonzero initial temperature. On the other hand, a GLOA defined in the interferometric phase approach through the purifications of the time-evolved density matrix, indeed shows that nonanalyiticies in the corresponding ``dynamical free-energy density'' persist, thereby establishing the existence of mixed state dynamical quantum phase transitions (MSDQPTs). Our work provides a framework that perfectly reproduces both the nonanalyticities and also the emergent topological structure in the pure state limit. These claims are corroborated by analyzing the nonequilibrium dynamics of a transverse Ising chain initially prepared in a thermal state and subjected to a sudden quench of the transverse field.

Colloquium: Nonequilibrium dynamics of closed interacting quantum systems

Abstract: This Colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems There is particularly a focus on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian Several aspects of the slow dynamics in driven systems are discussed and the universality of such dynamics in gapless systems with specific focus on dynamics near continuous quantum phase transitions is emphasized Recent progress on understanding thermalization in closed systems through the eigenstate thermalization hypothesis is also reviewed and relaxation in integrable systems is discussed Finally key experiments probing quantum dynamics in cold atom systems are overviewed and put into the context of our current theoretical understanding

Quantum Phase Transitions

Abstract: We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is tuned to a critical value are characterized by a dynamic exponent $z$ related to the energy and length scales $\Delta$ and $\xi$. Simple arguments based on an expansion to first order in the effective interaction allow to define an upper-critical dimension $D_{C}=4$ (where $D=d+z$ and $d$ is the spatial dimension) below which mean-field description is no longer valid. We emphasize the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems. Finally we quote some recent inelastic neutron scattering experiments performed on heavy-fermions which lead to unusual scaling law in $\omega /T$ for the dynamical spin susceptibility revealing critical local modes beyond the itinerant magnetism scheme and mention new attempts to describe this local quantum critical point.