Is there a relationship between large earthquakes (>M6) that occur along major fault zones and nearby volcanic eruptions?
Sometimes, yes. A few historic large regional earthquakes (>M 6) are considered by scientists to be related to a subsequent eruption or to some type of unrest at a nearby volcano. The exact triggering mechanism for these historic examples is not well understood, but the volcanic activity probably occurs in response to a change in the local pressure surrounding the magma reservoir system as a consequence of (1) severe ground shaking caused by the earthquake; or (2) a change in the "strain" or pressure in the Earth's crust in the region surrounding where the earthquake occurred.
For example, on November 29, 1975, a large magnitude-7.2 earthquake struck the Big Island of Hawaii at 4:48 a.m. It was centered about 28 kilometers southeast of Kilauea Volcano's summit caldera at a depth of 5 kilometers; the earthquake occurred within the volcano's south flank. The earthquake was preceded by numerous foreshocks, the largest of which was a 5.7 magnitude jolt at 3:36 a.m. the same morning, and was accompanied, or closely followed, by a tsunami, massive ground movements, hundreds of aftershocks, and a short-lived eruption in Kilauea's summit caldera.
The eruption began at 5:32 a.m. from a 500-meter long fissure on the caldera floor and ended by 10:00 p.m. According to scientists at the USGS Hawaiian Volcano Observatory, the eruptive activity "was apparently triggered by the 7.2 magnitude earthquake." The small volume and brief duration of the eruption suggest that the shallow magma might not have reached the surface under its own buoyant energy without a triggering mechanism apparently provided by the violent ground shaking.
At 04:48 HST that morning, a magnitude-7.7 earthquake shook the island and generated a local tsunami that killed 2 people. Strong shaking from the earthquake produced damage at many locations on the Island of Hawai‘i. Within Hawai‘i Volcanoes National Park, sections of Crater Rim Drive (shown in this photo) cracked, some slumped toward the crater. About a half hour later, a brief eruption took place within Kilauea caldera.