Publications

Continuous Wigner-Mott transition at ν=1/5

T. G. Kiely and Debanjan Chowdhury, preprint

Using infinite matrix product states (iMPS), we study the quantum flucutation-induced (zero-temperature) phase transition between a Wigner-Mott (WM) insulator and a metallic Fermi liquid at electronic filling ν=1/5 (corresponding to a total filling of 2/5). This particular WM insulator has both a spin and a charge gap, making it particularly amenable to study using an iMPS ansatz. On a two-leg-ladder geometry, we find that there is an intermediate gapless phase between the WM insulator and the gapless Luttinger liquid – a Luther-Emery liquid. This state is a one-dimensional analogue to a fluctuating superconductor: there is no gap to 2-particle Cooper pair excitations, but the single-electron excitation is gapped. This state often arises due to an attractive interaction. Here, we believe that this occurs due to residual pairing between spins in the WM insulating phase. On the five-leg cylinder, we find a direct transition between the Wigner-Mott and Fermi liquid phases. We argue that this transition is continuous due to a scaling collapse in the vicinity of the critical point. As the spin and charge gaps vanish simultaneously, the existence of a continuous transition is necessarily beyond the Landau-Ginzburg paradigm.

High-temperature transport in the one-dimensional mass-imbalanced Fermi-Hubbard model

Thomas G. Kiely and Erich J. Mueller, Phys. Rev. A 109, 063318 (2024)

The limit of high temperature is generically a simple starting point for calculations, as the infinite-temperature state is well-understood. Dynamics at high temperatures, however, are not necessarily so simple. Motivated by the difficulty of achieving low temperatures in ultracold atom systems, here we study the high-temperature transport properties of a 1D Fermi-Hubbard model with a mass imbalance. We find that, by tuning the mass imbalance, the model interpolates between two distinct integrable limits: a perfect metal and an insulator. Neither of these are what one usually expects in a high-temperature system. Using infinite matrix product state techniques, we quantitatively determine signatures of these states and study how relaxation timescales evolve as the mass imbalance is varied.

Role of conservation laws in the density matrix renormalization group

Thomas G. Kiely and Erich J. Mueller, Phys. Rev. B 106, 235126 (2022)

When modeling physical systems with global symmetries using matrix product states, one can encode the symmetry as a block-sparse constraint on the tensor products. This, in effect, constrains the accessible variational manifold to states that explicitly obey the imposed symmetry. Such techniques are indispensable when modeling finite-sized systems. In the thermodynamic limit, however, it is not obvious how such a constraint will interact with the tendency of systems to spontaneously break a symmetry. We study two examples of critical Luttinger liquids using infinite matrix product states with and without imposed symmetries. We determine that the relative performance of each variational state is a scaling function of the Luttinger parameter, and we quantify a variety of practical considerations.

Strong Increase in Ultrasound Attenuation Below Tc in Sr2RuO4: Possible Evidence for Domains

Sayak Ghosh, Thomas G. Kiely, Arkady Shekhter, F. Jerzembeck, N. Kikugawa, Dmitry A. Sokolov, A. P. Mackenzie, and B. J. Ramshaw, Phys. Rev. B 106, 024520 (2022)

Sr2RuO4 is a material with a number of unconventional properties. In particular, the nature of its superconducting gap is disputed. This paper reports on a study of ultrasound attenuation in Sr2RuO4 across the superconducting transition. The experiments, performed by Sayak Ghosh in the lab of Brad Ramshaw, found that the ultrasound attenuation constant increases as one decreases the temperature below Tc. My contribution to this work was to model this result, which disagrees with conventional s-wave BCS theory, using a variety of other gap functions. I found that an inversion-symmetry-breaking gap function (e.g. p-wave) can induce such a peak in the attenuation constant, but we determined that their observation is more likely due to domain wall fluctuations between regions with different superconducting order parameters.

Superfluidity in the one-dimensional Bose-Hubbard model

Thomas G. Kiely and Erich J. Mueller, Phys. Rev. B 105, 134502 (2022)

Superfluidity is a phenomenological property of systems with bosonic excitations that can loosely be understood as having zero viscosity. In three dimensions, systems that exhibit superfluidity often also exhibit phase coherence across macroscopic length scales, which is known as Bose-Einstein condensation. If the system is one-dimensional, however, strong quantum fluctuations destabilize such phase coherence – this is known as the Mermin-Wagner effect. Nonetheless, as we argue in this paper, superfluid phenomenology can persist. We study a paradigmatic strongly-interacting bosonic system, the 1D Bose-Hubbard model, using infinite tensor network techniques. We map out the superfluid density across the zero-temperature phase diagram and relate it to the Luttinger parameters.

Transport in the 2D Fermi-Hubbard Model: Lessons from Weak Coupling

Thomas G. Kiely and Erich J. Mueller, Phys. Rev. B 104, 165143 (2021) [Editor's Suggestion]

Strongly correlated materials, where electron-electron interactions dominate, display a range of important yet poorly understood phenomena including high temperature superconductivity and exotic magnetism. Many such materials also feature unusual “strange metal” transport, corresponding to unexpected temperature dependence of the resistivity. In this paper, we showed that weakly-interacting systems can display resistivity signatures typically associated with such strange metals. The origin of this effect is bandstructure nesting (at low temperatures) and a bounded spectrum (at high temperatures). These results are particularly important for interpreting recent cold atom experiments exploring transport in Fermi-Hubbard systems, as these experiments are constrained to operate at very high effective temperatures.

Relationship between the transverse-field Ising model and the XY model via the rotating-wave approximation

Thomas G. Kiely and J. K. Freericks, Phys. Rev. A 97, 023611 (2018)

Trapped ionic systems allow for long-lived realizations of one-dimensional Hamiltonians, which can serve both to answer basic science questions and to realize novel quantum mechanical devices, namely quantum computers. There are, however, certain limitations that experimentalists must contend with. One such limitation is in the nature of allowed interactions between the trapped ions, which can dramatically reduce the accessible range of applications. In this paper, we studied how the XY model (very difficult to engineer) emerges from the transverse-field Ising model (much easier to engineer) in the limit of a large transverse field. This trick has been used by the Monroe group to simulate the XY model stroboscopically. After demonstrating the general behavior of this approximation, we computed a variety of experimentally-relevant observables. Interestingly, we found that the strobosocopic approximation to the Greens function is particularly sensitive to experimental imperfections.

Thomas Kiely