Measuring the temperature of your coffee should not change the amount of coffee in your cup. This holds because the operators representing the coffee’s energy and volume commute. The intuitive assumption that conserved quantities, also known as charges, commute, underpins basic physics derivations, like that of the thermal state's form and Onsager coefficients. Yet, operators' failure to commute plays a key role in quantum theory, e.g. underlying uncertainty relations. Lifting this assumption has spawned a growing subfield of quantum many-body physics [1].
How can one argue that charges’ noncommutation caused a result? To isolate the effects of charges’ noncommutation, we created analogous models that differ in whether their charges commute and discovered more entanglement in the noncommuting-charge model [2]. We further introduce noncommuting charges (an SU(2) symmetry) into monitored quantum circuits, circuits with unitary evolutions and mid-circuit projective measurements. Numerically, we find that the SU(2)-symmetric model has a critical phase in place of the area-law phase typically found in these circuits [3]. I will focus on the results from Ref 2 and 3. Time permitting, I'll briefly explain how one can use Lie Algebra theory to build the Hamiltonians necessary for testing the predictions of noncommuting charge physics [4].
[1] Majidy et al. "Noncommuting conserved charges in quantum thermodynamics and beyond." Nat Rev Phys (2023)
[2] Majidy et al. "Non-Abelian symmetry can increase entanglement entropy.” PRB (2023)
[3] Majidy et al. "Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits." PRB (2023)
[4] Yunger Halpern and Majidy “How to build Hamiltonians that transport noncommuting charges in quantum thermodynamics” npj QI (2022)
We determine the low-energy spectrum and Parisi replica symmetry breaking function for the spin glass phase of the quantum Ising model with infinite-range random exchange interactions and transverse and longitudinal (h) fields. We show that, for all h, the spin glass state has full replica symmetry breaking, and the local spin spectrum is gapless with a spectral density which vanishes linearly with frequency. These results are obtained using an action functional - argued to yield exact results at low frequencies - that expands in powers of a spin glass order parameter, which is bilocal in time, and a matrix in replica space. We also present the exact solution of the infinite-range spherical quantum p-rotor model at nonzero h: here, the spin glass state has one-step replica symmetry breaking, and gaplessness only appears after imposition of an additional marginal stability condition.
Gravitational waves allow a glance into the properties and dynamics of the very early Universe.I will discuss the state-of-the-art of predicting a stochastic background of gravitational waves produced by cosmological first-order phase transitions.I focus on recent developments in understanding the dynamics of the primordial fluid and how to connect simulation results to observations and model building.Finally, I discuss the possibility to interpret the recent anomalies in pulsar timing arrays with this kind of signal
