Charge density waves in disordered media circumventing the Imry-Ma argument

Two powerful theoretical predictions, Anderson localization and the Imry-Ma argument, impose significant restrictions on the phases of matter that can exist in the presence of even the smallest amount of disorder in one-dimensional systems. These predictions forbid conducting states and ordered states respectively. It was thus remarkable that a mechanism to circumvent Anderson localization relying on the presence of correlated disorder was found, that is also realized in certain biomolecular systems. In a similar manner, we show that the Imry-Ma argument can be circumvented resulting in the formation of stable ordered states with discrete broken symmetries in disordered one dimensional systems. Specifically, we simulate a family of Hamiltonians of spinless fermions with correlated disorder and interactions, where we find that a charge density wave is stable up to a finite critical disorder strength. Having circumvented the Imry-Ma mechanism, we then investigate other mechanisms by which disorder can destroy an ordered state.