Since the 80s, strange metals, metals where the electrons are so densely entangled that the conventional condensed matter paradigm of Short Ranged Entanglement fails, have eluded any form of study...Show moreSince the 80s, strange metals, metals where the electrons are so densely entangled that the conventional condensed matter paradigm of Short Ranged Entanglement fails, have eluded any form of study due to the sign problem, which renders numerical calculations impossible. However, holography, a duality between strongly coupled quantum field theory problems and classical general relativity problems of one spatial dimension higher, grants us a way to circumvent the sign problem. In this thesis, we will run a modified version of code that was once used to simulate binary black holes on a supercomputer to calculate the properties of two $2+1$-dimensional holographic models for strange metals, the Reissner-Nordstr\"om metal and the Gubser-Rocha metal, subject to an ionic lattice potential: the code needed to simulate the Gubser-Rocha metal was only finished last year. We then investigate whether the DC electrical conductivity $\sigma$, thermopower $\alpha$ and thermal conductivity $\bar{\kappa}$ obey four different Drude models: one basic relativistic model and three models with different extra incoherent terms, models A, B and C. We find that model A, the most conventional model, fails, while the conductivities obey model C ($\kappa$-dominated transport) for low lattice strength $A$ and model B ($\sigma_{Q=0}$-dominated transport) for high $A$. We suspect this surprising result is caused by a pole collision causing a crossover between two regimes, but more research needs to be done to verify this.Show less
In the past decades experiments have found condensed matter systems which could not be described by the conventional methods of condensed matter theory, these are densely entangled strange metals....Show moreIn the past decades experiments have found condensed matter systems which could not be described by the conventional methods of condensed matter theory, these are densely entangled strange metals. During the same period, the string theory community has developed the AdS/CFT correspondence, a duality between field theories and gravitational systems. This duality may be used to understand condensed matter field theory from a gravitational perspective. It is especially useful for densely entangled quantum matter, which can be described according to the duality by charged black hole systems of classical gravity. In this thesis we will consider the Gubser-Rocha black hole of the Einstein-Maxwell-Dilaton action to describe a metal. To understand charge and heat transport in these metals, one needs a mechanism to dissipate momentum. This is explicitly implemented by introducing a periodic lattice in the condensed matter system. Using heavy numerical codes to calculate the gravitational differential equations that are dual to the metal, we can find the transport properties of our metal. In this metal a linear in T resistivity is found, which is a famous property of the strange metals. Furthermore we find empirically a saturation of the conductivity, which could be the instance of Planckian dissipation and the minimal viscosity of the strange metal.Show less
Weyl semimetals have been providing for a considerable research interest in the last decade in quantum condensed matter physics, due to their non-trivial topological nature and their possible...Show moreWeyl semimetals have been providing for a considerable research interest in the last decade in quantum condensed matter physics, due to their non-trivial topological nature and their possible applications in material science. Their non-trivial topological order has many consequences like zero energy Weyl nodes, which are robust to impurities and display a chiral anomaly. The work presented in this thesis is inspired by the intriguing matter of the response of Weyl semimetals to topological defects and their change to the behaviour of underlying lattice. To achieve this, we studied the response of different types of Weyl semimetals upon introducing a lattice dislocation or a pi-flux vortex, which mimics the effect of the former. Specifically, we show that the existence of a (or multiple) Kramers pair(s) of zero-energy modes bound to a dislocation line or vortex is a not a generic feature of topologically non-trivial phases of Weyl semimetals since this appears to depend on the present number of Weyl nodes and their chiralities as well as the type of symmetry breaking. We obtain the explicit form of these states, which shows their exponentially localised nature. Furthermore, we analyse the dependence of the energy of these dislocation modes on different parameters of the models and analyse the resulting correlations found. We then conclude by placing these results in a broader context.Show less
